Accurate Bollinger Bands mcbw_ [True Volatility Distribution]The Bollinger Bands have become a very important technical tool for discretionary and algorithmic traders alike over the last decades. It was designed to give traders an edge on the markets by setting probabilistic values to different levels of volatility. However, some of the assumptions that go into its calculations make it unusable for traders who want to get a correct understanding of the volatility that the bands are trying to be used for. Let's go through what the Bollinger Bands are said to show, how their calculations work, the problems in the calculations, and how the current indicator I am presenting today fixes these.
--> If you just want to know how the settings work then skip straight to the end or click on the little (i) symbol next to the values in the indicator settings window when its on your chart <--
--------------------------- What Are Bollinger Bands ---------------------------
The Bollinger Bands were formed in the 1980's, a time when many retail traders interacted with their symbols via physically printed charts and computer memory for personal computer memory was measured in Kb (about a factor of 1 million smaller than today). Bollinger Bands are designed to help a trader or algorithm see the likelihood of price expanding outside of its typical range, the further the lines are from the current price implies the less often they will get hit. With a hands on understanding many strategies use these levels for designated levels of breakout trades or to assist in defining price ranges.
--------------------------- How Bollinger Bands Work ---------------------------
The calculations that go into Bollinger Bands are rather simple. There is a moving average that centers the indicator and an equidistant top band and bottom band are drawn at a fixed width away. The moving average is just a typical moving average (or common variant) that tracks the price action, while the distance to the top and bottom bands is a direct function of recent price volatility. The way that the distance to the bands is calculated is inspired by formulas from statistics. The standard deviation is taken from the candles that go into the moving average and then this is multiplied by a user defined value to set the bands position, I will call this value 'the multiple'. When discussing Bollinger Bands, that trading community at large normally discusses 'the multiple' as a multiplier of the standard deviation as it applies to a normal distribution (gaußian probability). On a normal distribution the number of standard deviations away (which trades directly use as 'the multiple') you are directly corresponds to how likely/unlikely something is to happen:
1 standard deviation equals 68.3%, meaning that the price should stay inside the 1 standard deviation 68.3% of the time and be outside of it 31.7% of the time;
2 standard deviation equals 95.5%, meaning that the price should stay inside the 2 standard deviation 95.5% of the time and be outside of it 4.5% of the time;
3 standard deviation equals 99.7%, meaning that the price should stay inside the 3 standard deviation 99.7% of the time and be outside of it 0.3% of the time.
Therefore when traders set 'the multiple' to 2, they interpret this as meaning that price will not reach there 95.5% of the time.
---------------- The Problem With The Math of Bollinger Bands ----------------
In and of themselves the Bollinger Bands are a great tool, but they have become misconstrued with some incorrect sense of statistical meaning, when they should really just be taken at face value without any further interpretation or implication.
In order to explain this it is going to get a bit technical so I will give a little math background and try to simplify things. First let's review some statistics topics (distributions, percentiles, standard deviations) and then with that understanding explore the incorrect logic of how Bollinger Bands have been interpreted/employed.
---------------- Quick Stats Review ----------------
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(If you are comfortable with statistics feel free to skip ahead to the next section)
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-------- I: Probability distributions --------
When you have a lot of data it is helpful to see how many times different results appear in your dataset. To visualize this people use "histograms", which just shows how many times each element appears in the dataset by stacking each of the same elements on top of each other to form a graph. You may be familiar with the bell curve (also called the "normal distribution", which we will be calling it by). The normal distribution histogram looks like a big hump around zero and then drops off super quickly the further you get from it. This shape (the bell curve) is very nice because it has a lot of very nifty mathematical properties and seems to show up in nature all the time. Since it pops up in so many places, society has developed many different shortcuts related to it that speed up all kinds of calculations, including the shortcut that 1 standard deviation = 68.3%, 2 standard deviations = 95.5%, and 3 standard deviations = 99.7% (these only apply to the normal distribution). Despite how handy the normal distribution is and all the shortcuts we have for it are, and how much it shows up in the natural world, there is nothing that forces your specific dataset to look like it. In fact, your data can actually have any possible shape. As we will explore later, economic and financial datasets *rarely* follow the normal distribution.
-------- II: Percentiles --------
After you have made the histogram of your dataset you have built the "probability distribution" of your own dataset that is specific to all the data you have collected. There is a whole complicated framework for how to accurately calculate percentiles but we will dramatically simplify it for our use. The 'percentile' in our case is just the number of data points we are away from the "middle" of the data set (normally just 0). Lets say I took the difference of the daily close of a symbol for the last two weeks, green candles would be positive and red would be negative. In this example my dataset of day by day closing price difference is:
week 1:
week 2:
sorting all of these value into a single dataset I have:
I can separate the positive and negative returns and explore their distributions separately:
negative return distribution =
positive return distribution =
Taking the 25th% percentile of these would just be taking the value that is 25% towards the end of the end of these returns. Or akin the 100%th percentile would just be taking the vale that is 100% at the end of those:
negative return distribution (50%) = -5
positive return distribution (50%) = +4
negative return distribution (100%) = -10
positive return distribution (100%) = +20
Or instead of separating the positive and negative returns we can also look at all of the differences in the daily close as just pure price movement and not account for the direction, in this case we would pool all of the data together by ignoring the negative signs of the negative reruns
combined return distribution =
In this case the 50%th and 100%th percentile of the combined return distribution would be:
combined return distribution (50%) = 4
combined return distribution (100%) = 10
Sometimes taking the positive and negative distributions separately is better than pooling them into a combined distribution for some purposes. Other times the combined distribution is better.
Most financial data has very different distributions for negative returns and positive returns. This is encapsulated in sayings like "Price takes the stairs up and the elevator down".
-------- III: Standard Deviation --------
The formula for the standard deviation (refereed to here by its shorthand 'STDEV') can be intimidating, but going through each of its elements will illuminate what it does. The formula for STDEV is equal to:
square root ( (sum ) / N )
Going back the the dataset that you might have, the variables in the formula above are:
'mean' is the average of your entire dataset
'x' is just representative of a single point in your dataset (one point at a time)
'N' is the total number of things in your dataset.
Going back to the STDEV formula above we can see how each part of it works. Starting with the '(x - mean)' part. What this does is it takes every single point of the dataset and measure how far away it is from the mean of the entire dataset. Taking this value to the power of two: '(x - mean) ^ 2', means that points that are very far away from the dataset mean get 'penalized' twice as much. Points that are very close to the dataset mean are not impacted as much. In practice, this would mean that if your dataset had a bunch of values that were in a wide range but always stayed in that range, this value ('(x - mean) ^ 2') would end up being small. On the other hand, if your dataset was full of the exact same number, but had a couple outliers very far away, this would have a much larger value since the square par of '(x - mean) ^ 2' make them grow massive. Now including the sum part of 'sum ', this just adds up all the of the squared distanced from the dataset mean. Then this is divided by the number of values in the dataset ('N'), and then the square root of that value is taken.
There is nothing inherently special or definitive about the STDEV formula, it is just a tool with extremely widespread use and adoption. As we saw here, all the STDEV formula is really doing is measuring the intensity of the outliers.
--------------------------- Flaws of Bollinger Bands ---------------------------
The largest problem with Bollinger Bands is the assumption that price has a normal distribution. This is assumption is massively incorrect for many reasons that I will try to encapsulate into two points:
Price return do not follow a normal distribution, every single symbol on every single timeframe has is own unique distribution that is specific to only itself. Therefore all the tools, shortcuts, and ideas that we use for normal distributions do not apply to price returns, and since they do not apply here they should not be used. A more general approach is needed that allows each specific symbol on every specific timeframe to be treated uniquely.
The distributions of price returns on the positive and negative side are almost never the same. A more general approach is needed that allows positive and negative returns to be calculated separately.
In addition to the issues of the normal distribution assumption, the standard deviation formula (as shown above in the quick stats review) is essentially just a tame measurement of outliers (a more aggressive form of outlier measurement might be taking the differences to the power of 3 rather than 2). Despite this being a bit of a philosophical question, does the measurement of outlier intensity as defined by the STDEV formula really measure what we want to know as traders when we're experiencing volatility? Or would adjustments to that formula better reflect what we *experience* as volatility when we are actively trading? This is an open ended question that I will leave here, but I wanted to pose this question because it is a key part of what how the Bollinger Bands work that we all assume as a given.
Circling back on the normal distribution assumption, the standard deviation formula used in the calculation of the bands only encompasses the deviation of the candles that go into the moving average and have no knowledge of the historical price action. Therefore the level of the bands may not really reflect how the price action behaves over a longer period of time.
------------ Delivering Factually Accurate Data That Traders Need------------
In light of the problems identified above, this indicator fixes all of these issue and delivers statistically correct information that discretionary and algorithmic traders can use, with truly accurate probabilities. It takes the price action of the last 2,000 candles and builds a huge dataset of distributions that you can directly select your percentiles from. It also allows you to have the positive and negative distributions calculated separately, or if you would like, you can pool all of them together in a combined distribution. In addition to this, there is a wide selection of moving averages directly available in the indicator to choose from.
Hedge funds, quant shops, algo prop firms, and advanced mechanical groups all employ the true return distributions in their work. Now you have access to the same type of data with this indicator, wherein it's doing all the lifting for you.
------------------------------ Indicator Settings ------------------------------
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---- Moving average ----
Select the type of moving average you would like and its length
---- Bands ----
The percentiles that you enter here will be pulled directly from the return distribution of the last 2,000 candles. With the typical Bollinger Bands, traders would select 2 standard deviations and incorrectly think that the levels it highlights are the 95.5% levels. Now, if you want the true 95.5% level, you can just enter 95.5 into the percentile value here. Each of the three available bands takes the true percentile you enter here.
---- Separate Positive & Negative Distributions----
If this box is checked the positive and negative distributions are treated indecently, completely separate from each other. You will see that the width of the top and bottom bands will be different for each of the percentiles you enter.
If this box is unchecked then all the negative and positive distributions are pooled together. You will notice that the width of the top and bottom bands will be the exact same.
---- Distribution Size ----
This is the number of candles that the price return is calculated over. EG: to collect the price return over the last 33 candles, the difference of price from now to 33 candles ago is calculated for the last 2,000 candles, to build a return distribution of 2000 points of price differences over 33 candles.
NEGATIVE NUMBERS(<0) == exact number of candles to include;
EG: setting this value to -20 will always collect volatility distributions of 20 candles
POSITIVE NUMBERS(>0) == number of candles to include as a multiple of the Moving Average Length value set above;
EG: if the Moving Average Length value is set to 22, setting this value to 2 will use the last 22*2 = 44 candles for the collection of volatility distributions
MORE candles being include will generally make the bands WIDER and their size will change SLOWER over time.
I wish you focus, dedication, and earnest success on your journey.
Happy trading :)
Wyszukaj w skryptach "algo"
Intellect_city - Halvings Bitcoin CycleWhat is halving?
The halving timer shows when the next Bitcoin halving will occur, as well as the dates of past halvings. This event occurs every 210,000 blocks, which is approximately every 4 years. Halving reduces the emission reward by half. The original Bitcoin reward was 50 BTC per block found.
Why is halving necessary?
Halving allows you to maintain an algorithmically specified emission level. Anyone can verify that no more than 21 million bitcoins can be issued using this algorithm. Moreover, everyone can see how much was issued earlier, at what speed the emission is happening now, and how many bitcoins remain to be mined in the future. Even a sharp increase or decrease in mining capacity will not significantly affect this process. In this case, during the next difficulty recalculation, which occurs every 2014 blocks, the mining difficulty will be recalculated so that blocks are still found approximately once every ten minutes.
How does halving work in Bitcoin blocks?
The miner who collects the block adds a so-called coinbase transaction. This transaction has no entry, only exit with the receipt of emission coins to your address. If the miner's block wins, then the entire network will consider these coins to have been obtained through legitimate means. The maximum reward size is determined by the algorithm; the miner can specify the maximum reward size for the current period or less. If he puts the reward higher than possible, the network will reject such a block and the miner will not receive anything. After each halving, miners have to halve the reward they assign to themselves, otherwise their blocks will be rejected and will not make it to the main branch of the blockchain.
The impact of halving on the price of Bitcoin
It is believed that with constant demand, a halving of supply should double the value of the asset. In practice, the market knows when the halving will occur and prepares for this event in advance. Typically, the Bitcoin rate begins to rise about six months before the halving, and during the halving itself it does not change much. On average for past periods, the upper peak of the rate can be observed more than a year after the halving. It is almost impossible to predict future periods because, in addition to the reduction in emissions, many other factors influence the exchange rate. For example, major hacks or bankruptcies of crypto companies, the situation on the stock market, manipulation of “whales,” or changes in legislative regulation.
---------------------------------------------
Table - Past and future Bitcoin halvings:
---------------------------------------------
Date: Number of blocks: Award:
0 - 03-01-2009 - 0 block - 50 BTC
1 - 28-11-2012 - 210000 block - 25 BTC
2 - 09-07-2016 - 420000 block - 12.5 BTC
3 - 11-05-2020 - 630000 block - 6.25 BTC
4 - 20-04-2024 - 840000 block - 3.125 BTC
5 - 24-03-2028 - 1050000 block - 1.5625 BTC
6 - 26-02-2032 - 1260000 block - 0.78125 BTC
7 - 30-01-2036 - 1470000 block - 0.390625 BTC
8 - 03-01-2040 - 1680000 block - 0.1953125 BTC
9 - 07-12-2043 - 1890000 block - 0.09765625 BTC
10 - 10-11-2047 - 2100000 block - 0.04882813 BTC
11 - 14-10-2051 - 2310000 block - 0.02441406 BTC
12 - 17-09-2055 - 2520000 block - 0.01220703 BTC
13 - 21-08-2059 - 2730000 block - 0.00610352 BTC
14 - 25-07-2063 - 2940000 block - 0.00305176 BTC
15 - 28-06-2067 - 3150000 block - 0.00152588 BTC
16 - 01-06-2071 - 3360000 block - 0.00076294 BTC
17 - 05-05-2075 - 3570000 block - 0.00038147 BTC
18 - 08-04-2079 - 3780000 block - 0.00019073 BTC
19 - 12-03-2083 - 3990000 block - 0.00009537 BTC
20 - 13-02-2087 - 4200000 block - 0.00004768 BTC
21 - 17-01-2091 - 4410000 block - 0.00002384 BTC
22 - 21-12-2094 - 4620000 block - 0.00001192 BTC
23 - 24-11-2098 - 4830000 block - 0.00000596 BTC
24 - 29-10-2102 - 5040000 block - 0.00000298 BTC
25 - 02-10-2106 - 5250000 block - 0.00000149 BTC
26 - 05-09-2110 - 5460000 block - 0.00000075 BTC
27 - 09-08-2114 - 5670000 block - 0.00000037 BTC
28 - 13-07-2118 - 5880000 block - 0.00000019 BTC
29 - 16-06-2122 - 6090000 block - 0.00000009 BTC
30 - 20-05-2126 - 6300000 block - 0.00000005 BTC
31 - 23-04-2130 - 6510000 block - 0.00000002 BTC
32 - 27-03-2134 - 6720000 block - 0.00000001 BTC
Adaptive Fisherized Z-scoreHello Fellas,
It's time for a new adaptive fisherized indicator of me, where I apply adaptive length and more on a classic indicator.
Today, I chose the Z-score, also called standard score, as indicator of interest.
Special Features
Advanced Smoothing: JMA, T3, Hann Window and Super Smoother
Adaptive Length Algorithms: In-Phase Quadrature, Homodyne Discriminator, Median and Hilbert Transform
Inverse Fisher Transform (IFT)
Signals: Enter Long, Enter Short, Exit Long and Exit Short
Bar Coloring: Presents the trade state as bar colors
Band Levels: Changes the band levels
Decision Making
When you create such a mod you need to think about which concepts are the best to conclude. I decided to take Inverse Fisher Transform instead of normalization to make a version which fits to a fixed scale to avoid the usual distortion created by normalization.
Moreover, I chose JMA, T3, Hann Window and Super Smoother, because JMA and T3 are the bleeding-edge MA's at the moment with the best balance of lag and responsiveness. Additionally, I chose Hann Window and Super Smoother because of their extraordinary smoothing capabilities and because Ehlers favours them.
Furthermore, I decided to choose the half length of the dominant cycle instead of the full dominant cycle to make the indicator more responsive which is very important for a signal emitter like Z-score. Signal emitters always need to be faster or have the same speed as the filters they are combined with.
Usage
The Z-score is a low timeframe scalper which works best during choppy/ranging phases. The direction you should trade is determined by the last trend change. E.g. when the last trend change was from bearish market to bullish market and you are now in a choppy/ranging phase confirmed by e.g. Chop Zone or KAMA slope you want to do long trades.
Interpretation
The Z-score indicator is a momentum indicator which shows the number of standard deviations by which the value of a raw score (price/source) is above or below the mean value of what is being observed or measured. Easily explained, it is almost the same as Bollinger Bands with another visual representation form.
Signals
B -> Buy -> Z-score crosses above lower band
S -> Short -> Z-score crosses below upper band
BE -> Buy Exit -> Z-score crosses above 0
SE -> Sell Exit -> Z-score crosses below 0
If you were reading till here, thank you already. Now, follows a bunch of knowledge for people who don't know the concepts I talk about.
T3
The T3 moving average, short for "Tim Tillson's Triple Exponential Moving Average," is a technical indicator used in financial markets and technical analysis to smooth out price data over a specific period. It was developed by Tim Tillson, a software project manager at Hewlett-Packard, with expertise in Mathematics and Computer Science.
The T3 moving average is an enhancement of the traditional Exponential Moving Average (EMA) and aims to overcome some of its limitations. The primary goal of the T3 moving average is to provide a smoother representation of price trends while minimizing lag compared to other moving averages like Simple Moving Average (SMA), Weighted Moving Average (WMA), or EMA.
To compute the T3 moving average, it involves a triple smoothing process using exponential moving averages. Here's how it works:
Calculate the first exponential moving average (EMA1) of the price data over a specific period 'n.'
Calculate the second exponential moving average (EMA2) of EMA1 using the same period 'n.'
Calculate the third exponential moving average (EMA3) of EMA2 using the same period 'n.'
The formula for the T3 moving average is as follows:
T3 = 3 * (EMA1) - 3 * (EMA2) + (EMA3)
By applying this triple smoothing process, the T3 moving average is intended to offer reduced noise and improved responsiveness to price trends. It achieves this by incorporating multiple time frames of the exponential moving averages, resulting in a more accurate representation of the underlying price action.
JMA
The Jurik Moving Average (JMA) is a technical indicator used in trading to predict price direction. Developed by Mark Jurik, it’s a type of weighted moving average that gives more weight to recent market data rather than past historical data.
JMA is known for its superior noise elimination. It’s a causal, nonlinear, and adaptive filter, meaning it responds to changes in price action without introducing unnecessary lag. This makes JMA a world-class moving average that tracks and smooths price charts or any market-related time series with surprising agility.
In comparison to other moving averages, such as the Exponential Moving Average (EMA), JMA is known to track fast price movement more accurately. This allows traders to apply their strategies to a more accurate picture of price action.
Inverse Fisher Transform
The Inverse Fisher Transform is a transform used in DSP to alter the Probability Distribution Function (PDF) of a signal or in our case of indicators.
The result of using the Inverse Fisher Transform is that the output has a very high probability of being either +1 or –1. This bipolar probability distribution makes the Inverse Fisher Transform ideal for generating an indicator that provides clear buy and sell signals.
Hann Window
The Hann function (aka Hann Window) is named after the Austrian meteorologist Julius von Hann. It is a window function used to perform Hann smoothing.
Super Smoother
The Super Smoother uses a special mathematical process for the smoothing of data points.
The Super Smoother is a technical analysis indicator designed to be smoother and with less lag than a traditional moving average.
Adaptive Length
Length based on the dominant cycle length measured by a "dominant cycle measurement" algorithm.
Happy Trading!
Best regards,
simwai
---
Credits to
@cheatcountry
@everget
@loxx
@DasanC
@blackcat1402
Support & Resistance AI (K means/median) [ThinkLogicAI]█ OVERVIEW
K-means is a clustering algorithm commonly used in machine learning to group data points into distinct clusters based on their similarities. While K-means is not typically used directly for identifying support and resistance levels in financial markets, it can serve as a tool in a broader analysis approach.
Support and resistance levels are price levels in financial markets where the price tends to react or reverse. Support is a level where the price tends to stop falling and might start to rise, while resistance is a level where the price tends to stop rising and might start to fall. Traders and analysts often look for these levels as they can provide insights into potential price movements and trading opportunities.
█ BACKGROUND
The K-means algorithm has been around since the late 1950s, making it more than six decades old. The algorithm was introduced by Stuart Lloyd in his 1957 research paper "Least squares quantization in PCM" for telecommunications applications. However, it wasn't widely known or recognized until James MacQueen's 1967 paper "Some Methods for Classification and Analysis of Multivariate Observations," where he formalized the algorithm and referred to it as the "K-means" clustering method.
So, while K-means has been around for a considerable amount of time, it continues to be a widely used and influential algorithm in the fields of machine learning, data analysis, and pattern recognition due to its simplicity and effectiveness in clustering tasks.
█ COMPARE AND CONTRAST SUPPORT AND RESISTANCE METHODS
1) K-means Approach:
Cluster Formation: After applying the K-means algorithm to historical price change data and visualizing the resulting clusters, traders can identify distinct regions on the price chart where clusters are formed. Each cluster represents a group of similar price change patterns.
Cluster Analysis: Analyze the clusters to identify areas where clusters tend to form. These areas might correspond to regions of price behavior that repeat over time and could be indicative of support and resistance levels.
Potential Support and Resistance Levels: Based on the identified areas of cluster formation, traders can consider these regions as potential support and resistance levels. A cluster forming at a specific price level could suggest that this level has been historically significant, causing similar price behavior in the past.
Cluster Standard Deviation: In addition to looking at the means (centroids) of the clusters, traders can also calculate the standard deviation of price changes within each cluster. Standard deviation is a measure of the dispersion or volatility of data points around the mean. A higher standard deviation indicates greater price volatility within a cluster.
Low Standard Deviation: If a cluster has a low standard deviation, it suggests that prices within that cluster are relatively stable and less likely to exhibit sudden and large price movements. Traders might consider placing tighter stop-loss orders for trades within these clusters.
High Standard Deviation: Conversely, if a cluster has a high standard deviation, it indicates greater price volatility within that cluster. Traders might opt for wider stop-loss orders to allow for potential price fluctuations without getting stopped out prematurely.
Cluster Density: Each data point is assigned to a cluster so a cluster that is more dense will act more like gravity and
2) Traditional Approach:
Trendlines: Draw trendlines connecting significant highs or lows on a price chart to identify potential support and resistance levels.
Chart Patterns: Identify chart patterns like double tops, double bottoms, head and shoulders, and triangles that often indicate potential reversal points.
Moving Averages: Use moving averages to identify levels where the price might find support or resistance based on the average price over a specific period.
Psychological Levels: Identify round numbers or levels that traders often pay attention to, which can act as support and resistance.
Previous Highs and Lows: Identify significant previous price highs and lows that might act as support or resistance.
The key difference lies in the approach and the foundation of these methods. Traditional methods are based on well-established principles of technical analysis and market psychology, while the K-means approach involves clustering price behavior without necessarily incorporating market sentiment or specific price patterns.
It's important to note that while the K-means approach might provide an interesting way to analyze price data, it should be used cautiously and in conjunction with other traditional methods. Financial markets are influenced by a wide range of factors beyond just price behavior, and the effectiveness of any method for identifying support and resistance levels should be thoroughly tested and validated. Additionally, developments in trading strategies and analysis techniques could have occurred since my last update.
█ K MEANS ALGORITHM
The algorithm for K means is as follows:
Initialize cluster centers
assign data to clusters based on minimum distance
calculate cluster center by taking the average or median of the clusters
repeat steps 1-3 until cluster centers stop moving
█ LIMITATIONS OF K MEANS
There are 3 main limitations of this algorithm:
Sensitive to Initializations: K-means is sensitive to the initial placement of centroids. Different initializations can lead to different cluster assignments and final results.
Assumption of Equal Sizes and Variances: K-means assumes that clusters have roughly equal sizes and spherical shapes. This may not hold true for all types of data. It can struggle with identifying clusters with uneven densities, sizes, or shapes.
Impact of Outliers: K-means is sensitive to outliers, as a single outlier can significantly affect the position of cluster centroids. Outliers can lead to the creation of spurious clusters or distortion of the true cluster structure.
█ LIMITATIONS IN APPLICATION OF K MEANS IN TRADING
Trading data often exhibits characteristics that can pose challenges when applying indicators and analysis techniques. Here's how the limitations of outliers, varying scales, and unequal variance can impact the use of indicators in trading:
Outliers are data points that significantly deviate from the rest of the dataset. In trading, outliers can represent extreme price movements caused by rare events, news, or market anomalies. Outliers can have a significant impact on trading indicators and analyses:
Indicator Distortion: Outliers can skew the calculations of indicators, leading to misleading signals. For instance, a single extreme price spike could cause indicators like moving averages or RSI (Relative Strength Index) to give false signals.
Risk Management: Outliers can lead to overly aggressive trading decisions if not properly accounted for. Ignoring outliers might result in unexpected losses or missed opportunities to adjust trading strategies.
Different Scales: Trading data often includes multiple indicators with varying units and scales. For example, prices are typically in dollars, volume in units traded, and oscillators have their own scale. Mixing indicators with different scales can complicate analysis:
Normalization: Indicators on different scales need to be normalized or standardized to ensure they contribute equally to the analysis. Failure to do so can lead to one indicator dominating the analysis due to its larger magnitude.
Comparability: Without normalization, it's challenging to directly compare the significance of indicators. Some indicators might have a larger numerical range and could overshadow others.
Unequal Variance: Unequal variance in trading data refers to the fact that some indicators might exhibit higher volatility than others. This can impact the interpretation of signals and the performance of trading strategies:
Volatility Adjustment: When combining indicators with varying volatility, it's essential to adjust for their relative volatilities. Failure to do so might lead to overemphasizing or underestimating the importance of certain indicators in the trading strategy.
Risk Assessment: Unequal variance can impact risk assessment. Indicators with higher volatility might lead to riskier trading decisions if not properly taken into account.
█ APPLICATION OF THIS INDICATOR
This indicator can be used in 2 ways:
1) Make a directional trade:
If a trader thinks price will go higher or lower and price is within a cluster zone, The trader can take a position and place a stop on the 1 sd band around the cluster. As one can see below, the trader can go long the green arrow and place a stop on the one standard deviation mark for that cluster below it at the red arrow. using this we can calculate a risk to reward ratio.
Calculating risk to reward: targeting a risk reward ratio of 2:1, the trader could clearly make that given that the next resistance area above that in the orange cluster exceeds this risk reward ratio.
2) Take a reversal Trade:
We can use cluster centers (support and resistance levels) to go in the opposite direction that price is currently moving in hopes of price forming a pivot and reversing off this level.
Similar to the directional trade, we can use the standard deviation of the cluster to place a stop just in case we are wrong.
In this example below we can see that shorting on the red arrow and placing a stop at the one standard deviation above this cluster would give us a profitable trade with minimal risk.
Using the cluster density table in the upper right informs the trader just how dense the cluster is. Higher density clusters will give a higher likelihood of a pivot forming at these levels and price being rejected and switching direction with a larger move.
█ FEATURES & SETTINGS
General Settings:
Number of clusters: The user can select from 3 to five clusters. A good rule of thumb is that if you are trading intraday, less is more (Think 3 rather than 5). For daily 4 to 5 clusters is good.
Cluster Method: To get around the outlier limitation of k means clustering, The median was added. This gives the user the ability to choose either k means or k median clustering. K means is the preferred method if the user things there are no large outliers, and if there appears to be large outliers or it is assumed there are then K medians is preferred.
Bars back To train on: This will be the amount of bars to include in the clustering. This number is important so that the user includes bars that are recent but not so far back that they are out of the scope of where price can be. For example the last 2 years we have been in a range on the sp500 so 505 days in this setting would be more relevant than say looking back 5 years ago because price would have to move far to get there.
Show SD Bands: Select this to show the 1 standard deviation bands around the support and resistance level or unselect this to just show the support and resistance level by itself.
Features:
Besides the support and resistance levels and standard deviation bands, this indicator gives a table in the upper right hand corner to show the density of each cluster (support and resistance level) and is color coded to the cluster line on the chart. Higher density clusters mean price has been there previously more than lower density clusters and could mean a higher likelihood of a reversal when price reaches these areas.
█ WORKS CITED
Victor Sim, "Using K-means Clustering to Create Support and Resistance", 2020, towardsdatascience.com
Chris Piech, "K means", stanford.edu
█ ACKNOLWEDGMENTS
@jdehorty- Thanks for the publish template. It made organizing my thoughts and work alot easier.
Recursive Micro Zigzag🎲 Overview
Zigzag is basic building block for any pattern recognition algorithm. This indicator is a research-oriented tool that combines the concepts of Micro Zigzag and Recursive Zigzag to facilitate a comprehensive analysis of price patterns. This indicator focuses on deriving zigzag on multiple levels in more efficient and enhanced manner in order to support enhanced pattern recognition.
The Recursive Micro Zigzag Indicator utilises the Micro Zigzag as the foundation and applies the Recursive Zigzag technique to derive higher-level zigzags. By integrating these techniques, this indicator enables researchers to analyse price patterns at multiple levels and gain a deeper understanding of market behaviour.
🎲 Concept:
Micro Zigzag Base : The indicator utilises the Micro Zigzag concept to capture detailed price movements within each candle. It allows for the visualisation of the sequential price action within the candle, aiding in pattern recognition at a micro level.
Basic implementation of micro zigzag can be found in this link - Micro-Zigzag
Recursive Zigzag Expansion : Building upon the Micro Zigzag base, the indicator applies the Recursive Zigzag concept to derive higher-level zigzags. Through recursive analysis of the Micro Zigzag's pivots, the indicator uncovers intricate patterns and trends that may not be evident in single-level zigzags.
Earlier implementations of recursive zigzag can be found here:
Recursive Zigzag
Recursive Zigzag - Trendoscope
And the libraries
rZigzag
ZigzagMethods
The major differences in this implementation are
Micro Zigzag Base - Earlier implementation made use of standard zigzag as base whereas this implementation uses Micro Zigzag as base
Not cap on Pivot depth - Earlier implementation was limited by the depth of level 0 zigzag. In this implementation, we are trying to build the recursive algorithm progressively so that there is no cap on the depth of level 0 zigzag. But, if we go for higher levels, there is chance of program timing out due to pine limitations.
These algorithms are useful in automatically spotting patterns on the chart including Harmonic Patterns, Chart Patterns, Elliot Waves and many more.
Channel Based Zigzag [HeWhoMustNotBeNamed]🎲 Concept
Zigzag is built based on the price and number of offset bars. But, in this experiment, we build zigzag based on different bands such as Bollinger Band, Keltner Channel and Donchian Channel. The process is simple:
🎯 Derive bands based on input parameters
🎯 High of a bar is considered as pivot high only if the high price is above or equal to upper band.
🎯 Similarly low of a bar is considered as pivot low only if low price is below or equal to lower band.
🎯 Adding the pivot high/low follows same logic as that of regular zigzag where pivot high is always followed by pivot low and vice versa.
🎯 If the new pivot added is of same direction as that of last pivot, then both pivots are compared with each other and only the extreme one is kept. (Highest in case of pivot high and lowest in case of pivot low)
🎯 If a bar has both pivot high and pivot low - pivot with same direction as previous pivot is added to the list first before adding the pivot with opposite direction.
🎲 Use Cases
Can be used for pattern recognition algorithms instead of standard zigzag. This will help derive patterns which are relative to bands and channels.
Example: John Bollinger explains how to manually scan double tap using Bollinger Bands in this video: www.youtube.com This modified zigzag base can be used to achieve the same using algorithmic means.
🎲 Settings
Few simple configurations which will let you select the band properties. Notice that there is no zigzag length here. All the calculations depend on the bands.
With bands display, indicator looks something like this
Note that pivots do not always represent highest/lowest prices. They represent highest/lowest price relative to bands.
As mentioned many times, application of zigzag is not for buying at lower price and selling at higher price. It is mainly used for pattern recognition either manually or via algorithms. Lets build new Harmonic, Chart patterns, Trend Lines using the new zigzag?
cbndLibrary "cbnd"
Description:
A standalone Cumulative Bivariate Normal Distribution (CBND) functions that do not require any external libraries.
This includes 3 different CBND calculations: Drezner(1978), Drezner and Wesolowsky (1990), and Genz (2004)
Comments:
The standardized cumulative normal distribution function returns the probability that one random
variable is less than a and that a second random variable is less than b when the correlation
between the two variables is p. Since no closed-form solution exists for the bivariate cumulative
normal distribution, we present three approximations. The first one is the well-known
Drezner (1978) algorithm. The second one is the more efficient Drezner and Wesolowsky (1990)
algorithm. The third is the Genz (2004) algorithm, which is the most accurate one and therefore
our recommended algorithm. West (2005b) and Agca and Chance (2003) discuss the speed and
accuracy of bivariate normal distribution approximations for use in option pricing in
ore detail.
Reference:
The Complete Guide to Option Pricing Formulas, 2nd ed. (Espen Gaarder Haug)
CBND1(A, b, rho)
Returns the Cumulative Bivariate Normal Distribution (CBND) using Drezner 1978 Algorithm
Parameters:
A : float,
b : float,
rho : float,
Returns: float.
CBND2(A, b, rho)
Returns the Cumulative Bivariate Normal Distribution (CBND) using Drezner and Wesolowsky (1990) function
Parameters:
A : float,
b : float,
rho : float,
Returns: float.
CBND3(x, y, rho)
Returns the Cumulative Bivariate Normal Distribution (CBND) using Genz (2004) algorithm (this is the preferred method)
Parameters:
x : float,
y : float,
rho : float,
Returns: float.
STD-Stepped Fast Cosine Transform Moving Average [Loxx]STD-Stepped Fast Cosine Transform Moving Average is an experimental moving average that uses Fast Cosine Transform to calculate a moving average. This indicator has standard deviation stepping in order to smooth the trend by weeding out low volatility movements.
What is the Discrete Cosine Transform?
A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. The DCT, first proposed by Nasir Ahmed in 1972, is a widely used transformation technique in signal processing and data compression. It is used in most digital media, including digital images (such as JPEG and HEIF, where small high-frequency components can be discarded), digital video (such as MPEG and H.26x), digital audio (such as Dolby Digital, MP3 and AAC), digital television (such as SDTV, HDTV and VOD), digital radio (such as AAC+ and DAB+), and speech coding (such as AAC-LD, Siren and Opus). DCTs are also important to numerous other applications in science and engineering, such as digital signal processing, telecommunication devices, reducing network bandwidth usage, and spectral methods for the numerical solution of partial differential equations.
The use of cosine rather than sine functions is critical for compression, since it turns out (as described below) that fewer cosine functions are needed to approximate a typical signal, whereas for differential equations the cosines express a particular choice of boundary conditions. In particular, a DCT is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers. The DCTs are generally related to Fourier Series coefficients of a periodically and symmetrically extended sequence whereas DFTs are related to Fourier Series coefficients of only periodically extended sequences. DCTs are equivalent to DFTs of roughly twice the length, operating on real data with even symmetry (since the Fourier transform of a real and even function is real and even), whereas in some variants the input and/or output data are shifted by half a sample. There are eight standard DCT variants, of which four are common.
The most common variant of discrete cosine transform is the type-II DCT, which is often called simply "the DCT". This was the original DCT as first proposed by Ahmed. Its inverse, the type-III DCT, is correspondingly often called simply "the inverse DCT" or "the IDCT". Two related transforms are the discrete sine transform (DST), which is equivalent to a DFT of real and odd functions, and the modified discrete cosine transform (MDCT), which is based on a DCT of overlapping data. Multidimensional DCTs (MD DCTs) are developed to extend the concept of DCT to MD signals. There are several algorithms to compute MD DCT. A variety of fast algorithms have been developed to reduce the computational complexity of implementing DCT. One of these is the integer DCT (IntDCT), an integer approximation of the standard DCT, : ix, xiii, 1, 141–304 used in several ISO/IEC and ITU-T international standards.
Notable settings
windowper = period for calculation, restricted to powers of 2: "16", "32", "64", "128", "256", "512", "1024", "2048", this reason for this is FFT is an algorithm that computes DFT (Discrete Fourier Transform) in a fast way, generally in 𝑂(𝑁⋅log2(𝑁)) instead of 𝑂(𝑁2). To achieve this the input matrix has to be a power of 2 but many FFT algorithm can handle any size of input since the matrix can be zero-padded. For our purposes here, we stick to powers of 2 to keep this fast and neat. read more about this here: Cooley–Tukey FFT algorithm
smthper = smoothing count, this smoothing happens after the first FCT regular pass. this zeros out frequencies from the previously calculated values above SS count. the lower this number, the smoother the output, it works opposite from other smoothing periods
Included
Alerts
Signals
Loxx's Expanded Source Types
Additional reading
A Fast Computational Algorithm for the Discrete Cosine Transform by Chen et al.
Practical Fast 1-D DCT Algorithms With 11 Multiplications by Loeffler et al.
Cooley–Tukey FFT algorithm
Weighted Burg AR Spectral Estimate Extrapolation of Price [Loxx]Weighted Burg AR Spectral Estimate Extrapolation of Price is an indicator that uses an autoregressive spectral estimation called the Weighted Burg Algorithm. This method is commonly used in speech modeling and speech prediction engines. This method also includes Levinson–Durbin algorithm. As was already discussed previously in the following indicator:
Levinson-Durbin Autocorrelation Extrapolation of Price
What is Levinson recursion or Levinson–Durbin recursion?
In many applications, the duration of an uninterrupted measurement of a time series is limited. However, it is often possible to obtain several separate segments of data. The estimation of an autoregressive model from this type of data is discussed. A straightforward approach is to take the average of models estimated from each segment separately. In this way, the variance of the estimated parameters is reduced. However, averaging does not reduce the bias in the estimate. With the Burg algorithm for segments, both the variance and the bias in the estimated parameters are reduced by fitting a single model to all segments simultaneously. As a result, the model estimated with the Burg algorithm for segments is more accurate than models obtained with averaging. The new weighted Burg algorithm for segments allows combining segments of different amplitudes.
The Burg algorithm estimates the AR parameters by determining reflection coefficients that minimize the sum of for-ward and backward residuals. The extension of the algorithm to segments is that the reflection coefficients are estimated by minimizing the sum of forward and backward residuals of all segments taken together. This means a single model is fitted to all segments in one time. This concept is also used for prediction error methods in system identification, where the input to the system is known, like in ARX modeling
Data inputs
Source Settings: -Loxx's Expanded Source Types. You typically use "open" since open has already closed on the current active bar
LastBar - bar where to start the prediction
PastBars - how many bars back to model
LPOrder - order of linear prediction model; 0 to 1
FutBars - how many bars you want to forward predict
BurgWin - weighing function index, rectangular, hamming, or parabolic
Things to know
Normally, a simple moving average is calculated on source data. I've expanded this to 38 different averaging methods using Loxx's Moving Avreages.
This indicator repaints
Included
Bar color muting
Further reading
Performance of the weighted burg methods of ar spectral estimation for pitch-synchronous analysis of voiced speech
The Burg algorithm for segments
Techniques for the Enhancement of Linear Predictive Speech Coding in Adverse Conditions
Related Indicators
Synthetic Price Action GeneratorNOTICE:
First thing you need to know, it "DOES NOT" reflect the price of the ticker you will load it on. THIS IS NOT AN INDICATOR FOR TRADING! It's a developer tool solely generating random values that look exactly like the fractals we observe every single day. This script's generated candles are as fake as the never ending garbage news cycles we are often force fed and expected to believe by using carefully scripted narratives peddled as hypnotic truth to psychologically and emotionally influence you to the point of control by coercion and subjugation. I wanted to make the script's synthetic nature very clear using that analogy, it's dynamically artificial. Do not accidentally become disillusioned by this scripts values, make trading decisions from it, and lastly don't become victim to predatory media magic ministry parrots with pretty, handsome smiles, compelling you to board their ferris wheel of fear. Now, on to the good stuff...
BACKSTORY:
Occasionally I find myself in situations where I have to build analyzers in Pine to actually build novel quantitative analytic indicators and tools worthy of future use. These analyzers certainly don't exist on this platform, but usually are required to engineer and tweak algorithms of the highest quality with the finest computational caliber. I have numerous other synthesizers to publish besides this one.
For many reasons, I needed a synthetic environment to utilize the analyzers I built in Pine, to even pursue building some exotic indicators and algorithms. Pine doesn't allow sourcing of tuples. Not to mention, I required numerous Pine advancements to make long held dreams into tangible realities. Many Pine upgrades have arrived and MANY, MANY more are in need of implementation for all. Now that I have this, intending to use it in the future often when in need, you can now use it too. I do anticipate some skilled Pine poets will employ this intended handy utility to design and/or improved indicators for trading.
ORIGIN:
This was inspired by the brilliance from the world renowned ALGOmist John F. Ehlers, but it's taken on a completely alien form from its original DNA. Browsing on the internet for something else, I came across an article with a small code snippet, and I remembered an old wish of mine. I have long known that by flipping back and forth on specific tickers and timeframes in my Watchlist is not the most efficient way to evaluate indicators in multiple theatres of price action. I realized, I always wanted to possess and use this sort of tool, so... I put it into Pine form, but now have decided to inject it with Pine Script steroids. The outcome is highly mutable candle formations in a reusable mutagenic package, observable above and masquerading as genuine looking price candles.
OVERVIEW:
I guess you could call it a price action synthesizer, but I entitled it "Synthetic Price Action Generator" for those who may be searching for such a thing. You may find this more useful on the All or 5Y charts initially to witness indication from beginning (barstate.isfirst === barindex==0) to end (last_bar_index), but you may also use keyboard shortcuts + + to view the earliest plottable bars on any timeframe. I often use that keyboard shortcut to qualify an indicator through the entirety of it's runtime.
A lot can go wrong unexpectedly with indicator initialization, and you will never know it if you don't inspect it. Many recursively endowed Infinite Impulse Response (IIR) Filters can initialize with unintended results that minutely ring in slightly erroneous fashion for the entire runtime, beginning to end, causing deviations from "what should of been..." values with false signals. Looking closely at spg(), you will recognize that 3 EMAs are employed to manage and maintain randomness of CLOSE, HIGH, and LOW. In fact, any indicator's barindex==0 initialization can be inspected with the keyboard shortcuts above. If you see anything obviously strange in an authors indicator, please contact the developer if possible and respectfully notify them.
PURPOSE:
The primary intended application of this script, is to offer developers from advanced to even novice skill levels assistance with building next generation indicators. Mostly, it's purpose is for testing and troubleshooting indicators AND evaluating how they perform in a "manageable" randomized environment. Some times indicators flake out on rare but problematic price fluctuations, and this may help you with finding your issues/errata sooner than later. While the candles upon initial loading look pristine, by tweaking it to the minval/maxval parameters limits OR beyond with a few code modifications, you can generate unusual volatility, for instance... huge wicks. Limits of minval= and maxval= of are by default set to a comfort zone of operation. Massive wicks or candle bodies will undoubtedly affect your indication and often render them useless on tickers that exhibit that behavior, like WGMCF intraday currently.
Copy/paste boundaries are provided for relevant insertion into another script. Paste placement should happen at the very top of a script. Note that by overwriting the close, open, high, etc... values, your compiler will give you generous warnings of "variable shadowing" in abundance, but this is an expected part of applying it to your novel script, no worries. plotcandle() can be copied over too and enabled/disabled in Settings->Style. Always remember to fully remove this scripts' code and those assignments properly before actual trading use of your script occurs, AND specifically when publishing. The entirety of this provided code should never, never exist in a published indicator.
OTHER INTENTIONS:
Even though these are 100% synthetic generated price points, you will notice ALL of the fractal pseudo-patterns that commonly exist in the markets, are naturally occurring with this generator too. You can also swiftly immerse yourself in pattern recognition exercises with increased efficiency in real time by clicking any SPAG Setting in focus and then using the up/down arrow keys. I hope I explained potential uses adequately...
On a personal note, the existence of fractal symmetry often makes me wonder, do we truly live in a totality chaotic universe or is it ordered mathematically for some outcomes to a certain extent. I think both. My observations, it's a pre-deterministic reality completely influenced by infinitesimal amounts of sentient free will with unimaginable existing and emerging quantities. Some how an unknown mysterious mechanism governing the totality of universal physics and mathematics counts this 100.0% flawlessly and perpetually. Anyways, you can't change the past that long existed before your birth or even yesterday, but you can choose to dream, create, and forge the future into your desires and hopes. As always, shite always happens when your not looking for it. What you choose to do after stepping in it unintentionally... is totally up to you. :) Maybe this tool and tips provided will aid you in not stepping in an algo cachucha up to your ankles somehow.
SCRIPTING LESSONS PORTRAYED IN THIS SCRIPT:
Pine etiquette and code cleanliness
Overwrite capabilities of built-in Pine variables for testing indicators
Various techniques to organize Settings panel while providing ease of adjustment utility
Use of tooltip= to provide users adequate valuable information. Most people want to trade with indicators, not blindly make adjustments to them without any knowledge of their intended operation/effects
When available time provides itself, I will consider your inquiries, thoughts, and concepts presented below in the comments section, should you have any questions or comments regarding this indicator. When my indicators achieve more prevalent use by TV members , I may implement more ideas when they present themselves as worthy additions. Have a profitable future everyone!
the "fasle" hull moving averageThere is a little different between my "fasle hull moving average" the "correct one".
the correct algorithm:
hma = wma((2*wma(close,n/2) - wma(close,n),sqrt(n))
the "fasle" algorithm:
=wma((2*wma(close,n/4) - wma(close,n),sqrt(n))
Amazing! Why the "fasle" describe the trend so accurate!?
ICT SIlver Bullet Trading Windows UK times🎯 Purpose of the Indicator
It’s designed to highlight key ICT “macro” and “micro” windows of opportunity, i.e., time ranges where liquidity grabs and algorithmic setups are most likely to occur. The ICT Silver Bullet concept is built on the idea that institutions execute in recurring intraday windows, and these often produce high-probability setups.
🕰️ Windows
London Macro Window
10:00 – 11:00 UK time
This aligns with a major liquidity window after the London equities open settles and London + EU traders reposition.
You’re looking for setups like liquidity sweeps, MSS (market structure shift), and FVG entries here.
New York Macro Window
15:00 – 16:00 UK time (10:00 – 11:00 NY time)
This is right after the NY equities open, a key ICT window for volatility and liquidity grabs.
Power Hour
Usually 20:00 – 21:00 UK time (3pm–4pm NY time), the last trading hour of NY equities.
ICT often refers to this as another manipulation window where setups can form before the daily close.
🔍 What the Indicator Does
Draws session boxes or shading: so you can visually see the London/NY/Power Hour windows directly on your chart.
Macro vs. Micro time frames:
Macro windows → The ones you set (London & NY) are the major daily algo execution windows.
Micro windows → Within those boxes, ICT expects smaller intraday setups (like a Silver Bullet entry from a sweep + FVG).
Guides your trade selection: it tells you when not to hunt trades everywhere, but instead to wait for price action confirmation inside those boxes.
🧩 How This Fits ICT Silver Bullet Trading
The ICT Silver Bullet strategy says:
Wait for one of the macro windows (London or NY).
Look for liquidity sweep → market structure shift → FVG.
Enter with defined risk inside that hour.
This indicator essentially does step 1 for you: it makes those high-probability windows visually obvious, so you don’t waste time trading random hours where algos aren’t active.
Harmonic Patterns + Fib [CRT Trader]Overview
The Harmonic Patterns Fibonacci indicator is an advanced technical analysis tool designed to automatically detect and visualize Fibonacci-based harmonic patterns on financial charts. This indicator helps traders identify high-probability reversal zones and potential entry/exit points based on precise mathematical relationships.
Supported Patterns
5-Point Patterns (X-A-B-C-D Structure)
Gartley Pattern: The most common harmonic pattern with reliable reversal signals
AB/XA = 0.618, BC/AB = 0.618, CD/BC = 1.272, AD/XA = 0.786
Butterfly Pattern: Strong reversal pattern indicating potential trend changes
AB/XA = 0.786, BC/AB = 0.618, CD/BC = 1.618, AD/XA = 1.270
Bat Pattern: Medium-term reversal pattern with high accuracy
AB/XA = 0.382, BC/AB = 0.886, CD/BC = 1.618, AD/XA = 0.886
Crab Pattern: Aggressive reversal pattern with extended D point
AB/XA = 0.618, BC/AB = 0.886, CD/BC = 2.240, AD/XA = 1.618
Shark Pattern: Trend continuation or reversal pattern
AB/XA = 0.618, BC/AB = 1.130, CD/BC = 1.618, AD/XA = 0.886
4-Point Pattern (A-B-C-D Structure)
ABCD Pattern: Basic harmonic structure forming the foundation of all patterns
BC/AB = 0.382-0.886, CD/BC = 1.130-2.618
Key Features
Fibonacci Validation
Each pattern is validated against precise Fibonacci ratios with customizable tolerance
Mathematical accuracy ensures reliable pattern recognition
Eliminates false signals through strict ratio requirements
Performance Optimization
Pivot Detection: Automatically identifies significant highs and lows
Scan Frequency Control: Adjustable scanning intervals to optimize performance
Early Exit Algorithms: Efficient computation to reduce processing load
Pattern Limit: Control maximum number of patterns displayed
Visual Elements
Pattern Lines: Clear visualization of pattern structure with colored lines
Fill Areas: Highlighted zones between pattern legs
Point Labels: X, A, B, C, D markers for easy identification
Fibonacci Levels: Optional Fibonacci retracement/extension levels
Bullish/Bearish Colors: Green for bullish, red for bearish patterns
Customizable Settings
Pattern Selection: Enable/disable specific pattern types
Tolerance Adjustment: Fine-tune pattern recognition sensitivity (5-30%)
Color Customization: Personalize visual appearance
Information Table: Optional statistics display
Trading Applications
Entry Signals
Reversal Zones: Identify high-probability reversal areas at pattern completion
Confluence Trading: Combine with other technical indicators for confirmation
Risk Management: Use pattern structure to define stop-loss levels
Market Analysis
Support/Resistance: Pattern points often act as future S/R levels
Price Targets: Fibonacci extensions provide potential profit targets
Market Structure: Understand underlying market geometry and rhythm
Strategy Integration
Swing Trading: Ideal for medium-term position entries
Position Trading: Long-term trend reversal identification
Day Trading: Intraday reversal patterns on lower timeframes
How to Use
Add to Chart: Apply the indicator to any timeframe and instrument
Configure Settings: Adjust tolerance, colors, and pattern types as needed
Wait for Completion: Patterns are valid only when D point is formed
Confirm with Volume: Look for volume confirmation at pattern completion
Set Stop Loss: Place stops beyond X point for 5-point patterns, or A point for ABCD
Target Levels: Use Fibonacci extensions for profit targets
Important Notes
Pattern Completion: Wait for full pattern formation before taking action
Market Context: Consider overall market trend and conditions
Risk Management: Always use appropriate position sizing and stops
Backtesting: Test the indicator on historical data before live trading
Multiple Timeframes: Analyze patterns across different timeframes for confirmation
Technical Requirements
Lookback Period: Adjustable pivot detection sensitivity
Depth Setting: Controls how far back the algorithm searches for patterns
Memory Efficient: Optimized for real-time performance without lag
This indicator is suitable for all experience levels, from beginners learning harmonic patterns to advanced traders seeking automated pattern recognition. The combination of mathematical precision and visual clarity makes it an essential tool for harmonic trading strategies.
Auto-Fit Growth Trendline# **Theoretical Algorithmic Principles of the Auto-Fit Growth Trendline (AFGT)**
## **🎯 What Does This Algorithm Do?**
The Auto-Fit Growth Trendline is an advanced technical analysis system that **automates the identification of long-term growth trends** and **projects future price levels** based on historical cyclical patterns.
### **Primary Functionality:**
- **Automatically detects** the most significant lows in regular periods (monthly, quarterly, semi-annually, annually)
- **Constructs a dynamic trendline** that connects these historical lows
- **Projects the trend into the future** with high mathematical precision
- **Generates Fibonacci bands** that act as dynamic support and resistance levels
- **Automatically adapts** to different timeframes and market conditions
### **Strategic Purpose:**
The algorithm is designed to identify **fundamental value zones** where price has historically found support, enabling traders to:
- Identify optimal entry points for long positions
- Establish realistic price targets based on mathematical projections
- Recognize dynamic support and resistance levels
- Anticipate long-term price movements
---
## **🧮 Core Mathematical Foundations**
### **Adaptive Temporal Segmentation Theory**
The algorithm is based on **dynamic temporal partition theory**, where time is divided into mathematically coherent uniform intervals. It uses modular transformations to create bijective mappings between continuous timestamps and discrete periods, ensuring each temporal point belongs uniquely to a specific period.
**What does this achieve?** It allows the algorithm to automatically identify natural market cycles (annual, quarterly, etc.) without manual intervention, adapting to the inherent periodicity of each asset.
The temporal mapping function implements a **discrete affine transformation** that normalizes different frequencies (monthly, quarterly, semi-annual, annual) to a space of unique identifiers, enabling consistent cross-temporal comparative analysis.
---
## **📊 Local Extrema Detection Theory**
### **Multi-Point Retrospective Validation Principle**
Local minima detection is founded on **relative extrema theory with sliding window**. Instead of using a simple minimum finder, it implements a cross-validation system that examines the persistence of the extremum across multiple historical periods.
**What problem does this solve?** It eliminates false minima caused by temporal volatility, identifying only those points that represent true historical support levels with statistical significance.
This approach is based on the **statistical confirmation principle**, where a minimum is only considered valid if it maintains its extremum condition during a defined observation period, significantly reducing false positives caused by transitory volatility.
---
## **🔬 Robust Interpolation Theory with Outlier Control**
### **Contextual Adaptive Interpolation Model**
The mathematical core uses **piecewise linear interpolation with adaptive outlier correction**. The key innovation lies in implementing a **contextual anomaly detector** that identifies not only absolute extreme values, but relative deviations to the local context.
**Why is this important?** Financial markets contain extreme events (crashes, bubbles) that can distort projections. This system identifies and appropriately weights them without completely eliminating them, preserving directional information while attenuating distortions.
### **Implicit Bayesian Smoothing Algorithm**
When an outlier is detected (deviation >300% of local average), the system applies a **simplified Kalman filter** that combines the current observation with a local trend estimation, using a weight factor that preserves directional information while attenuating extreme fluctuations.
---
## **📈 Stabilized Extrapolation Theory**
### **Exponential Growth Model with Dampening**
Extrapolation is based on a **modified exponential growth model with progressive dampening**. It uses multiple historical points to calculate local growth ratios, implements statistical filtering to eliminate outliers, and applies a dampening factor that increases with extrapolation distance.
**What advantage does this offer?** Long-term projections in finance tend to be exponentially unrealistic. This system maintains short-to-medium term accuracy while converging toward realistic long-term projections, avoiding the typical "exponential explosions" of other methods.
### **Asymptotic Convergence Principle**
For long-term projections, the algorithm implements **controlled asymptotic convergence**, where growth ratios gradually converge toward pre-established limits, avoiding unrealistic exponential projections while preserving short-to-medium term accuracy.
---
## **🌟 Dynamic Fibonacci Projection Theory**
### **Continuous Proportional Scaling Model**
Fibonacci bands are constructed through **uniform proportional scaling** of the base curve, where each level represents a linear transformation of the main curve by a constant factor derived from the Fibonacci sequence.
**What is its practical utility?** It provides dynamic resistance and support levels that move with the trend, offering price targets and profit-taking points that automatically adapt to market evolution.
### **Topological Preservation Principle**
The system maintains the **topological properties** of the base curve in all Fibonacci projections, ensuring that spatial and temporal relationships are consistently preserved across all resistance/support levels.
---
## **⚡ Adaptive Computational Optimization**
### **Multi-Scale Resolution Theory**
It implements **automatic multi-resolution analysis** where data granularity is dynamically adjusted according to the analysis timeframe. It uses the **adaptive Nyquist principle** to optimize the signal-to-noise ratio according to the temporal observation scale.
**Why is this necessary?** Different timeframes require different levels of detail. A 1-minute chart needs more granularity than a monthly one. This system automatically optimizes resolution for each case.
### **Adaptive Density Algorithm**
Calculation point density is optimized through **adaptive sampling theory**, where calculation frequency is adjusted according to local trend curvature and analysis timeframe, balancing visual precision with computational efficiency.
---
## **🛡️ Robustness and Fault Tolerance**
### **Graceful Degradation Theory**
The system implements **multi-level graceful degradation**, where under error conditions or insufficient data, the algorithm progressively falls back to simpler but reliable methods, maintaining basic functionality under any condition.
**What does this guarantee?** That the indicator functions consistently even with incomplete data, new symbols with limited history, or extreme market conditions.
### **State Consistency Principle**
It uses **mathematical invariants** to guarantee that the algorithm's internal state remains consistent between executions, implementing consistency checks that validate data structure integrity in each iteration.
---
## **🔍 Key Theoretical Innovations**
### **A. Contextual vs. Absolute Outlier Detection**
It revolutionizes traditional outlier detection by considering not only the absolute magnitude of deviations, but their relative significance within the local context of the time series.
**Practical impact:** It distinguishes between legitimate market movements and technical anomalies, preserving important events like breakouts while filtering noise.
### **B. Extrapolation with Weighted Historical Memory**
It implements a memory system that weights different historical periods according to their relevance for current prediction, creating projections more adaptable to market regime changes.
**Competitive advantage:** It automatically adapts to fundamental changes in asset dynamics without requiring manual recalibration.
### **C. Automatic Multi-Timeframe Adaptation**
It develops an automatic temporal resolution selection system that optimizes signal extraction according to the intrinsic characteristics of the analysis timeframe.
**Result:** A single indicator that functions optimally from 1-minute to monthly charts without manual adjustments.
### **D. Intelligent Asymptotic Convergence**
It introduces the concept of controlled asymptotic convergence in financial extrapolations, where long-term projections converge toward realistic limits based on historical fundamentals.
**Added value:** Mathematically sound long-term projections that avoid the unrealistic extremes typical of other extrapolation methods.
---
## **📊 Complexity and Scalability Theory**
### **Optimized Linear Complexity Model**
The algorithm maintains **linear computational complexity** O(n) in the number of historical data points, guaranteeing scalability for extensive time series analysis without performance degradation.
### **Temporal Locality Principle**
It implements **temporal locality**, where the most expensive operations are concentrated in the most relevant temporal regions (recent periods and near projections), optimizing computational resource usage.
---
## **🎯 Convergence and Stability**
### **Probabilistic Convergence Theory**
The system guarantees **probabilistic convergence** toward the real underlying trend, where projection accuracy increases with the amount of available historical data, following **law of large numbers** principles.
**Practical implication:** The more history an asset has, the more accurate the algorithm's projections will be.
### **Guaranteed Numerical Stability**
It implements **intrinsic numerical stability** through the use of robust floating-point arithmetic and validations that prevent overflow, underflow, and numerical error propagation.
**Result:** Reliable operation even with extreme-priced assets (from satoshis to thousand-dollar stocks).
---
## **💼 Comprehensive Practical Application**
**The algorithm functions as a "financial GPS"** that:
1. **Identifies where we've been** (significant historical lows)
2. **Determines where we are** (current position relative to the trend)
3. **Projects where we're going** (future trend with specific price levels)
4. **Provides alternative routes** (Fibonacci bands as alternative targets)
This theoretical framework represents an innovative synthesis of time series analysis, approximation theory, and computational optimization, specifically designed for long-term financial trend analysis with robust and mathematically grounded projections.
Tensor Market Analysis Engine (TMAE)# Tensor Market Analysis Engine (TMAE)
## Advanced Multi-Dimensional Mathematical Analysis System
*Where Quantum Mathematics Meets Market Structure*
---
## 🎓 THEORETICAL FOUNDATION
The Tensor Market Analysis Engine represents a revolutionary synthesis of three cutting-edge mathematical frameworks that have never before been combined for comprehensive market analysis. This indicator transcends traditional technical analysis by implementing advanced mathematical concepts from quantum mechanics, information theory, and fractal geometry.
### 🌊 Multi-Dimensional Volatility with Jump Detection
**Hawkes Process Implementation:**
The TMAE employs a sophisticated Hawkes process approximation for detecting self-exciting market jumps. Unlike traditional volatility measures that treat price movements as independent events, the Hawkes process recognizes that market shocks cluster and exhibit memory effects.
**Mathematical Foundation:**
```
Intensity λ(t) = μ + Σ α(t - Tᵢ)
```
Where market jumps at times Tᵢ increase the probability of future jumps through the decay function α, controlled by the Hawkes Decay parameter (0.5-0.99).
**Mahalanobis Distance Calculation:**
The engine calculates volatility jumps using multi-dimensional Mahalanobis distance across up to 5 volatility dimensions:
- **Dimension 1:** Price volatility (standard deviation of returns)
- **Dimension 2:** Volume volatility (normalized volume fluctuations)
- **Dimension 3:** Range volatility (high-low spread variations)
- **Dimension 4:** Correlation volatility (price-volume relationship changes)
- **Dimension 5:** Microstructure volatility (intrabar positioning analysis)
This creates a volatility state vector that captures market behavior impossible to detect with traditional single-dimensional approaches.
### 📐 Hurst Exponent Regime Detection
**Fractal Market Hypothesis Integration:**
The TMAE implements advanced Rescaled Range (R/S) analysis to calculate the Hurst exponent in real-time, providing dynamic regime classification:
- **H > 0.6:** Trending (persistent) markets - momentum strategies optimal
- **H < 0.4:** Mean-reverting (anti-persistent) markets - contrarian strategies optimal
- **H ≈ 0.5:** Random walk markets - breakout strategies preferred
**Adaptive R/S Analysis:**
Unlike static implementations, the TMAE uses adaptive windowing that adjusts to market conditions:
```
H = log(R/S) / log(n)
```
Where R is the range of cumulative deviations and S is the standard deviation over period n.
**Dynamic Regime Classification:**
The system employs hysteresis to prevent regime flipping, requiring sustained Hurst values before regime changes are confirmed. This prevents false signals during transitional periods.
### 🔄 Transfer Entropy Analysis
**Information Flow Quantification:**
Transfer entropy measures the directional flow of information between price and volume, revealing lead-lag relationships that indicate future price movements:
```
TE(X→Y) = Σ p(yₜ₊₁, yₜ, xₜ) log
```
**Causality Detection:**
- **Volume → Price:** Indicates accumulation/distribution phases
- **Price → Volume:** Suggests retail participation or momentum chasing
- **Balanced Flow:** Market equilibrium or transition periods
The system analyzes multiple lag periods (2-20 bars) to capture both immediate and structural information flows.
---
## 🔧 COMPREHENSIVE INPUT SYSTEM
### Core Parameters Group
**Primary Analysis Window (10-100, Default: 50)**
The fundamental lookback period affecting all calculations. Optimization by timeframe:
- **1-5 minute charts:** 20-30 (rapid adaptation to micro-movements)
- **15 minute-1 hour:** 30-50 (balanced responsiveness and stability)
- **4 hour-daily:** 50-100 (smooth signals, reduced noise)
- **Asset-specific:** Cryptocurrency 20-35, Stocks 35-50, Forex 40-60
**Signal Sensitivity (0.1-2.0, Default: 0.7)**
Master control affecting all threshold calculations:
- **Conservative (0.3-0.6):** High-quality signals only, fewer false positives
- **Balanced (0.7-1.0):** Optimal risk-reward ratio for most trading styles
- **Aggressive (1.1-2.0):** Maximum signal frequency, requires careful filtering
**Signal Generation Mode:**
- **Aggressive:** Any component signals (highest frequency)
- **Confluence:** 2+ components agree (balanced approach)
- **Conservative:** All 3 components align (highest quality)
### Volatility Jump Detection Group
**Volatility Dimensions (2-5, Default: 3)**
Determines the mathematical space complexity:
- **2D:** Price + Volume volatility (suitable for clean markets)
- **3D:** + Range volatility (optimal for most conditions)
- **4D:** + Correlation volatility (advanced multi-asset analysis)
- **5D:** + Microstructure volatility (maximum sensitivity)
**Jump Detection Threshold (1.5-4.0σ, Default: 3.0σ)**
Standard deviations required for volatility jump classification:
- **Cryptocurrency:** 2.0-2.5σ (naturally volatile)
- **Stock Indices:** 2.5-3.0σ (moderate volatility)
- **Forex Major Pairs:** 3.0-3.5σ (typically stable)
- **Commodities:** 2.0-3.0σ (varies by commodity)
**Jump Clustering Decay (0.5-0.99, Default: 0.85)**
Hawkes process memory parameter:
- **0.5-0.7:** Fast decay (jumps treated as independent)
- **0.8-0.9:** Moderate clustering (realistic market behavior)
- **0.95-0.99:** Strong clustering (crisis/event-driven markets)
### Hurst Exponent Analysis Group
**Calculation Method Options:**
- **Classic R/S:** Original Rescaled Range (fast, simple)
- **Adaptive R/S:** Dynamic windowing (recommended for trading)
- **DFA:** Detrended Fluctuation Analysis (best for noisy data)
**Trending Threshold (0.55-0.8, Default: 0.60)**
Hurst value defining persistent market behavior:
- **0.55-0.60:** Weak trend persistence
- **0.65-0.70:** Clear trending behavior
- **0.75-0.80:** Strong momentum regimes
**Mean Reversion Threshold (0.2-0.45, Default: 0.40)**
Hurst value defining anti-persistent behavior:
- **0.35-0.45:** Weak mean reversion
- **0.25-0.35:** Clear ranging behavior
- **0.15-0.25:** Strong reversion tendency
### Transfer Entropy Parameters Group
**Information Flow Analysis:**
- **Price-Volume:** Classic flow analysis for accumulation/distribution
- **Price-Volatility:** Risk flow analysis for sentiment shifts
- **Multi-Timeframe:** Cross-timeframe causality detection
**Maximum Lag (2-20, Default: 5)**
Causality detection window:
- **2-5 bars:** Immediate causality (scalping)
- **5-10 bars:** Short-term flow (day trading)
- **10-20 bars:** Structural flow (swing trading)
**Significance Threshold (0.05-0.3, Default: 0.15)**
Minimum entropy for signal generation:
- **0.05-0.10:** Detect subtle information flows
- **0.10-0.20:** Clear causality only
- **0.20-0.30:** Very strong flows only
---
## 🎨 ADVANCED VISUAL SYSTEM
### Tensor Volatility Field Visualization
**Five-Layer Resonance Bands:**
The tensor field creates dynamic support/resistance zones that expand and contract based on mathematical field strength:
- **Core Layer (Purple):** Primary tensor field with highest intensity
- **Layer 2 (Neutral):** Secondary mathematical resonance
- **Layer 3 (Info Blue):** Tertiary harmonic frequencies
- **Layer 4 (Warning Gold):** Outer field boundaries
- **Layer 5 (Success Green):** Maximum field extension
**Field Strength Calculation:**
```
Field Strength = min(3.0, Mahalanobis Distance × Tensor Intensity)
```
The field amplitude adjusts to ATR and mathematical distance, creating dynamic zones that respond to market volatility.
**Radiation Line Network:**
During active tensor states, the system projects directional radiation lines showing field energy distribution:
- **8 Directional Rays:** Complete angular coverage
- **Tapering Segments:** Progressive transparency for natural visual flow
- **Pulse Effects:** Enhanced visualization during volatility jumps
### Dimensional Portal System
**Portal Mathematics:**
Dimensional portals visualize regime transitions using category theory principles:
- **Green Portals (◉):** Trending regime detection (appear below price for support)
- **Red Portals (◎):** Mean-reverting regime (appear above price for resistance)
- **Yellow Portals (○):** Random walk regime (neutral positioning)
**Tensor Trail Effects:**
Each portal generates 8 trailing particles showing mathematical momentum:
- **Large Particles (●):** Strong mathematical signal
- **Medium Particles (◦):** Moderate signal strength
- **Small Particles (·):** Weak signal continuation
- **Micro Particles (˙):** Signal dissipation
### Information Flow Streams
**Particle Stream Visualization:**
Transfer entropy creates flowing particle streams indicating information direction:
- **Upward Streams:** Volume leading price (accumulation phases)
- **Downward Streams:** Price leading volume (distribution phases)
- **Stream Density:** Proportional to information flow strength
**15-Particle Evolution:**
Each stream contains 15 particles with progressive sizing and transparency, creating natural flow visualization that makes information transfer immediately apparent.
### Fractal Matrix Grid System
**Multi-Timeframe Fractal Levels:**
The system calculates and displays fractal highs/lows across five Fibonacci periods:
- **8-Period:** Short-term fractal structure
- **13-Period:** Intermediate-term patterns
- **21-Period:** Primary swing levels
- **34-Period:** Major structural levels
- **55-Period:** Long-term fractal boundaries
**Triple-Layer Visualization:**
Each fractal level uses three-layer rendering:
- **Shadow Layer:** Widest, darkest foundation (width 5)
- **Glow Layer:** Medium white core line (width 3)
- **Tensor Layer:** Dotted mathematical overlay (width 1)
**Intelligent Labeling System:**
Smart spacing prevents label overlap using ATR-based minimum distances. Labels include:
- **Fractal Period:** Time-based identification
- **Topological Class:** Mathematical complexity rating (0, I, II, III)
- **Price Level:** Exact fractal price
- **Mahalanobis Distance:** Current mathematical field strength
- **Hurst Exponent:** Current regime classification
- **Anomaly Indicators:** Visual strength representations (○ ◐ ● ⚡)
### Wick Pressure Analysis
**Rejection Level Mathematics:**
The system analyzes candle wick patterns to project future pressure zones:
- **Upper Wick Analysis:** Identifies selling pressure and resistance zones
- **Lower Wick Analysis:** Identifies buying pressure and support zones
- **Pressure Projection:** Extends lines forward based on mathematical probability
**Multi-Layer Glow Effects:**
Wick pressure lines use progressive transparency (1-8 layers) creating natural glow effects that make pressure zones immediately visible without cluttering the chart.
### Enhanced Regime Background
**Dynamic Intensity Mapping:**
Background colors reflect mathematical regime strength:
- **Deep Transparency (98% alpha):** Subtle regime indication
- **Pulse Intensity:** Based on regime strength calculation
- **Color Coding:** Green (trending), Red (mean-reverting), Neutral (random)
**Smoothing Integration:**
Regime changes incorporate 10-bar smoothing to prevent background flicker while maintaining responsiveness to genuine regime shifts.
### Color Scheme System
**Six Professional Themes:**
- **Dark (Default):** Professional trading environment optimization
- **Light:** High ambient light conditions
- **Classic:** Traditional technical analysis appearance
- **Neon:** High-contrast visibility for active trading
- **Neutral:** Minimal distraction focus
- **Bright:** Maximum visibility for complex setups
Each theme maintains mathematical accuracy while optimizing visual clarity for different trading environments and personal preferences.
---
## 📊 INSTITUTIONAL-GRADE DASHBOARD
### Tensor Field Status Section
**Field Strength Display:**
Real-time Mahalanobis distance calculation with dynamic emoji indicators:
- **⚡ (Lightning):** Extreme field strength (>1.5× threshold)
- **● (Solid Circle):** Strong field activity (>1.0× threshold)
- **○ (Open Circle):** Normal field state
**Signal Quality Rating:**
Democratic algorithm assessment:
- **ELITE:** All 3 components aligned (highest probability)
- **STRONG:** 2 components aligned (good probability)
- **GOOD:** 1 component active (moderate probability)
- **WEAK:** No clear component signals
**Threshold and Anomaly Monitoring:**
- **Threshold Display:** Current mathematical threshold setting
- **Anomaly Level (0-100%):** Combined volatility and volume spike measurement
- **>70%:** High anomaly (red warning)
- **30-70%:** Moderate anomaly (orange caution)
- **<30%:** Normal conditions (green confirmation)
### Tensor State Analysis Section
**Mathematical State Classification:**
- **↑ BULL (Tensor State +1):** Trending regime with bullish bias
- **↓ BEAR (Tensor State -1):** Mean-reverting regime with bearish bias
- **◈ SUPER (Tensor State 0):** Random walk regime (neutral)
**Visual State Gauge:**
Five-circle progression showing tensor field polarity:
- **🟢🟢🟢⚪⚪:** Strong bullish mathematical alignment
- **⚪⚪🟡⚪⚪:** Neutral/transitional state
- **⚪⚪🔴🔴🔴:** Strong bearish mathematical alignment
**Trend Direction and Phase Analysis:**
- **📈 BULL / 📉 BEAR / ➡️ NEUTRAL:** Primary trend classification
- **🌪️ CHAOS:** Extreme information flow (>2.0 flow strength)
- **⚡ ACTIVE:** Strong information flow (1.0-2.0 flow strength)
- **😴 CALM:** Low information flow (<1.0 flow strength)
### Trading Signals Section
**Real-Time Signal Status:**
- **🟢 ACTIVE / ⚪ INACTIVE:** Long signal availability
- **🔴 ACTIVE / ⚪ INACTIVE:** Short signal availability
- **Components (X/3):** Active algorithmic components
- **Mode Display:** Current signal generation mode
**Signal Strength Visualization:**
Color-coded component count:
- **Green:** 3/3 components (maximum confidence)
- **Aqua:** 2/3 components (good confidence)
- **Orange:** 1/3 components (moderate confidence)
- **Gray:** 0/3 components (no signals)
### Performance Metrics Section
**Win Rate Monitoring:**
Estimated win rates based on signal quality with emoji indicators:
- **🔥 (Fire):** ≥60% estimated win rate
- **👍 (Thumbs Up):** 45-59% estimated win rate
- **⚠️ (Warning):** <45% estimated win rate
**Mathematical Metrics:**
- **Hurst Exponent:** Real-time fractal dimension (0.000-1.000)
- **Information Flow:** Volume/price leading indicators
- **📊 VOL:** Volume leading price (accumulation/distribution)
- **💰 PRICE:** Price leading volume (momentum/speculation)
- **➖ NONE:** Balanced information flow
- **Volatility Classification:**
- **🔥 HIGH:** Above 1.5× jump threshold
- **📊 NORM:** Normal volatility range
- **😴 LOW:** Below 0.5× jump threshold
### Market Structure Section (Large Dashboard)
**Regime Classification:**
- **📈 TREND:** Hurst >0.6, momentum strategies optimal
- **🔄 REVERT:** Hurst <0.4, contrarian strategies optimal
- **🎲 RANDOM:** Hurst ≈0.5, breakout strategies preferred
**Mathematical Field Analysis:**
- **Dimensions:** Current volatility space complexity (2D-5D)
- **Hawkes λ (Lambda):** Self-exciting jump intensity (0.00-1.00)
- **Jump Status:** 🚨 JUMP (active) / ✅ NORM (normal)
### Settings Summary Section (Large Dashboard)
**Active Configuration Display:**
- **Sensitivity:** Current master sensitivity setting
- **Lookback:** Primary analysis window
- **Theme:** Active color scheme
- **Method:** Hurst calculation method (Classic R/S, Adaptive R/S, DFA)
**Dashboard Sizing Options:**
- **Small:** Essential metrics only (mobile/small screens)
- **Normal:** Balanced information density (standard desktop)
- **Large:** Maximum detail (multi-monitor setups)
**Position Options:**
- **Top Right:** Standard placement (avoids price action)
- **Top Left:** Wide chart optimization
- **Bottom Right:** Recent price focus (scalping)
- **Bottom Left:** Maximum price visibility (swing trading)
---
## 🎯 SIGNAL GENERATION LOGIC
### Multi-Component Convergence System
**Component Signal Architecture:**
The TMAE generates signals through sophisticated component analysis rather than simple threshold crossing:
**Volatility Component:**
- **Jump Detection:** Mahalanobis distance threshold breach
- **Hawkes Intensity:** Self-exciting process activation (>0.2)
- **Multi-dimensional:** Considers all volatility dimensions simultaneously
**Hurst Regime Component:**
- **Trending Markets:** Price above SMA-20 with positive momentum
- **Mean-Reverting Markets:** Price at Bollinger Band extremes
- **Random Markets:** Bollinger squeeze breakouts with directional confirmation
**Transfer Entropy Component:**
- **Volume Leadership:** Information flow from volume to price
- **Volume Spike:** Volume 110%+ above 20-period average
- **Flow Significance:** Above entropy threshold with directional bias
### Democratic Signal Weighting
**Signal Mode Implementation:**
- **Aggressive Mode:** Any single component triggers signal
- **Confluence Mode:** Minimum 2 components must agree
- **Conservative Mode:** All 3 components must align
**Momentum Confirmation:**
All signals require momentum confirmation:
- **Long Signals:** RSI >50 AND price >EMA-9
- **Short Signals:** RSI <50 AND price 0.6):**
- **Increase Sensitivity:** Catch momentum continuation
- **Lower Mean Reversion Threshold:** Avoid counter-trend signals
- **Emphasize Volume Leadership:** Institutional accumulation/distribution
- **Tensor Field Focus:** Use expansion for trend continuation
- **Signal Mode:** Aggressive or Confluence for trend following
**Range-Bound Markets (Hurst <0.4):**
- **Decrease Sensitivity:** Avoid false breakouts
- **Lower Trending Threshold:** Quick regime recognition
- **Focus on Price Leadership:** Retail sentiment extremes
- **Fractal Grid Emphasis:** Support/resistance trading
- **Signal Mode:** Conservative for high-probability reversals
**Volatile Markets (High Jump Frequency):**
- **Increase Hawkes Decay:** Recognize event clustering
- **Higher Jump Threshold:** Avoid noise signals
- **Maximum Dimensions:** Capture full volatility complexity
- **Reduce Position Sizing:** Risk management adaptation
- **Enhanced Visuals:** Maximum information for rapid decisions
**Low Volatility Markets (Low Jump Frequency):**
- **Decrease Jump Threshold:** Capture subtle movements
- **Lower Hawkes Decay:** Treat moves as independent
- **Reduce Dimensions:** Simplify analysis
- **Increase Position Sizing:** Capitalize on compressed volatility
- **Minimal Visuals:** Reduce distraction in quiet markets
---
## 🚀 ADVANCED TRADING STRATEGIES
### The Mathematical Convergence Method
**Entry Protocol:**
1. **Fractal Grid Approach:** Monitor price approaching significant fractal levels
2. **Tensor Field Confirmation:** Verify field expansion supporting direction
3. **Portal Signal:** Wait for dimensional portal appearance
4. **ELITE/STRONG Quality:** Only trade highest quality mathematical signals
5. **Component Consensus:** Confirm 2+ components agree in Confluence mode
**Example Implementation:**
- Price approaching 21-period fractal high
- Tensor field expanding upward (bullish mathematical alignment)
- Green portal appears below price (trending regime confirmation)
- ELITE quality signal with 3/3 components active
- Enter long position with stop below fractal level
**Risk Management:**
- **Stop Placement:** Below/above fractal level that generated signal
- **Position Sizing:** Based on Mahalanobis distance (higher distance = smaller size)
- **Profit Targets:** Next fractal level or tensor field resistance
### The Regime Transition Strategy
**Regime Change Detection:**
1. **Monitor Hurst Exponent:** Watch for persistent moves above/below thresholds
2. **Portal Color Change:** Regime transitions show different portal colors
3. **Background Intensity:** Increasing regime background intensity
4. **Mathematical Confirmation:** Wait for regime confirmation (hysteresis)
**Trading Implementation:**
- **Trending Transitions:** Trade momentum breakouts, follow trend
- **Mean Reversion Transitions:** Trade range boundaries, fade extremes
- **Random Transitions:** Trade breakouts with tight stops
**Advanced Techniques:**
- **Multi-Timeframe:** Confirm regime on higher timeframe
- **Early Entry:** Enter on regime transition rather than confirmation
- **Regime Strength:** Larger positions during strong regime signals
### The Information Flow Momentum Strategy
**Flow Detection Protocol:**
1. **Monitor Transfer Entropy:** Watch for significant information flow shifts
2. **Volume Leadership:** Strong edge when volume leads price
3. **Flow Acceleration:** Increasing flow strength indicates momentum
4. **Directional Confirmation:** Ensure flow aligns with intended trade direction
**Entry Signals:**
- **Volume → Price Flow:** Enter during accumulation/distribution phases
- **Price → Volume Flow:** Enter on momentum confirmation breaks
- **Flow Reversal:** Counter-trend entries when flow reverses
**Optimization:**
- **Scalping:** Use immediate flow detection (2-5 bar lag)
- **Swing Trading:** Use structural flow (10-20 bar lag)
- **Multi-Asset:** Compare flow between correlated assets
### The Tensor Field Expansion Strategy
**Field Mathematics:**
The tensor field expansion indicates mathematical pressure building in market structure:
**Expansion Phases:**
1. **Compression:** Field contracts, volatility decreases
2. **Tension Building:** Mathematical pressure accumulates
3. **Expansion:** Field expands rapidly with directional movement
4. **Resolution:** Field stabilizes at new equilibrium
**Trading Applications:**
- **Compression Trading:** Prepare for breakout during field contraction
- **Expansion Following:** Trade direction of field expansion
- **Reversion Trading:** Fade extreme field expansion
- **Multi-Dimensional:** Consider all field layers for confirmation
### The Hawkes Process Event Strategy
**Self-Exciting Jump Trading:**
Understanding that market shocks cluster and create follow-on opportunities:
**Jump Sequence Analysis:**
1. **Initial Jump:** First volatility jump detected
2. **Clustering Phase:** Hawkes intensity remains elevated
3. **Follow-On Opportunities:** Additional jumps more likely
4. **Decay Period:** Intensity gradually decreases
**Implementation:**
- **Jump Confirmation:** Wait for mathematical jump confirmation
- **Direction Assessment:** Use other components for direction
- **Clustering Trades:** Trade subsequent moves during high intensity
- **Decay Exit:** Exit positions as Hawkes intensity decays
### The Fractal Confluence System
**Multi-Timeframe Fractal Analysis:**
Combining fractal levels across different periods for high-probability zones:
**Confluence Zones:**
- **Double Confluence:** 2 fractal levels align
- **Triple Confluence:** 3+ fractal levels cluster
- **Mathematical Confirmation:** Tensor field supports the level
- **Information Flow:** Transfer entropy confirms direction
**Trading Protocol:**
1. **Identify Confluence:** Find 2+ fractal levels within 1 ATR
2. **Mathematical Support:** Verify tensor field alignment
3. **Signal Quality:** Wait for STRONG or ELITE signal
4. **Risk Definition:** Use fractal level for stop placement
5. **Profit Targeting:** Next major fractal confluence zone
---
## ⚠️ COMPREHENSIVE RISK MANAGEMENT
### Mathematical Position Sizing
**Mahalanobis Distance Integration:**
Position size should inversely correlate with mathematical field strength:
```
Position Size = Base Size × (Threshold / Mahalanobis Distance)
```
**Risk Scaling Matrix:**
- **Low Field Strength (<2.0):** Standard position sizing
- **Moderate Field Strength (2.0-3.0):** 75% position sizing
- **High Field Strength (3.0-4.0):** 50% position sizing
- **Extreme Field Strength (>4.0):** 25% position sizing or no trade
### Signal Quality Risk Adjustment
**Quality-Based Position Sizing:**
- **ELITE Signals:** 100% of planned position size
- **STRONG Signals:** 75% of planned position size
- **GOOD Signals:** 50% of planned position size
- **WEAK Signals:** No position or paper trading only
**Component Agreement Scaling:**
- **3/3 Components:** Full position size
- **2/3 Components:** 75% position size
- **1/3 Components:** 50% position size or skip trade
### Regime-Adaptive Risk Management
**Trending Market Risk:**
- **Wider Stops:** Allow for trend continuation
- **Trend Following:** Trade with regime direction
- **Higher Position Size:** Trend probability advantage
- **Momentum Stops:** Trail stops based on momentum indicators
**Mean-Reverting Market Risk:**
- **Tighter Stops:** Quick exits on trend continuation
- **Contrarian Positioning:** Trade against extremes
- **Smaller Position Size:** Higher reversal failure rate
- **Level-Based Stops:** Use fractal levels for stops
**Random Market Risk:**
- **Breakout Focus:** Trade only clear breakouts
- **Tight Initial Stops:** Quick exit if breakout fails
- **Reduced Frequency:** Skip marginal setups
- **Range-Based Targets:** Profit targets at range boundaries
### Volatility-Adaptive Risk Controls
**High Volatility Periods:**
- **Reduced Position Size:** Account for wider price swings
- **Wider Stops:** Avoid noise-based exits
- **Lower Frequency:** Skip marginal setups
- **Faster Exits:** Take profits more quickly
**Low Volatility Periods:**
- **Standard Position Size:** Normal risk parameters
- **Tighter Stops:** Take advantage of compressed ranges
- **Higher Frequency:** Trade more setups
- **Extended Targets:** Allow for compressed volatility expansion
### Multi-Timeframe Risk Alignment
**Higher Timeframe Trend:**
- **With Trend:** Standard or increased position size
- **Against Trend:** Reduced position size or skip
- **Neutral Trend:** Standard position size with tight management
**Risk Hierarchy:**
1. **Primary:** Current timeframe signal quality
2. **Secondary:** Higher timeframe trend alignment
3. **Tertiary:** Mathematical field strength
4. **Quaternary:** Market regime classification
---
## 📚 EDUCATIONAL VALUE AND MATHEMATICAL CONCEPTS
### Advanced Mathematical Concepts
**Tensor Analysis in Markets:**
The TMAE introduces traders to tensor analysis, a branch of mathematics typically reserved for physics and advanced engineering. Tensors provide a framework for understanding multi-dimensional market relationships that scalar and vector analysis cannot capture.
**Information Theory Applications:**
Transfer entropy implementation teaches traders about information flow in markets, a concept from information theory that quantifies directional causality between variables. This provides intuition about market microstructure and participant behavior.
**Fractal Geometry in Trading:**
The Hurst exponent calculation exposes traders to fractal geometry concepts, helping understand that markets exhibit self-similar patterns across multiple timeframes. This mathematical insight transforms how traders view market structure.
**Stochastic Process Theory:**
The Hawkes process implementation introduces concepts from stochastic process theory, specifically self-exciting point processes. This provides mathematical framework for understanding why market events cluster and exhibit memory effects.
### Learning Progressive Complexity
**Beginner Mathematical Concepts:**
- **Volatility Dimensions:** Understanding multi-dimensional analysis
- **Regime Classification:** Learning market personality types
- **Signal Democracy:** Algorithmic consensus building
- **Visual Mathematics:** Interpreting mathematical concepts visually
**Intermediate Mathematical Applications:**
- **Mahalanobis Distance:** Statistical distance in multi-dimensional space
- **Rescaled Range Analysis:** Fractal dimension measurement
- **Information Entropy:** Quantifying uncertainty and causality
- **Field Theory:** Understanding mathematical fields in market context
**Advanced Mathematical Integration:**
- **Tensor Field Dynamics:** Multi-dimensional market force analysis
- **Stochastic Self-Excitation:** Event clustering and memory effects
- **Categorical Composition:** Mathematical signal combination theory
- **Topological Market Analysis:** Understanding market shape and connectivity
### Practical Mathematical Intuition
**Developing Market Mathematics Intuition:**
The TMAE serves as a bridge between abstract mathematical concepts and practical trading applications. Traders develop intuitive understanding of:
- **How markets exhibit mathematical structure beneath apparent randomness**
- **Why multi-dimensional analysis reveals patterns invisible to single-variable approaches**
- **How information flows through markets in measurable, predictable ways**
- **Why mathematical models provide probabilistic edges rather than certainties**
---
## 🔬 IMPLEMENTATION AND OPTIMIZATION
### Getting Started Protocol
**Phase 1: Observation (Week 1)**
1. **Apply with defaults:** Use standard settings on your primary trading timeframe
2. **Study visual elements:** Learn to interpret tensor fields, portals, and streams
3. **Monitor dashboard:** Observe how metrics change with market conditions
4. **No trading:** Focus entirely on pattern recognition and understanding
**Phase 2: Pattern Recognition (Week 2-3)**
1. **Identify signal patterns:** Note what market conditions produce different signal qualities
2. **Regime correlation:** Observe how Hurst regimes affect signal performance
3. **Visual confirmation:** Learn to read tensor field expansion and portal signals
4. **Component analysis:** Understand which components drive signals in different markets
**Phase 3: Parameter Optimization (Week 4-5)**
1. **Asset-specific tuning:** Adjust parameters for your specific trading instrument
2. **Timeframe optimization:** Fine-tune for your preferred trading timeframe
3. **Sensitivity adjustment:** Balance signal frequency with quality
4. **Visual customization:** Optimize colors and intensity for your trading environment
**Phase 4: Live Implementation (Week 6+)**
1. **Paper trading:** Test signals with hypothetical trades
2. **Small position sizing:** Begin with minimal risk during learning phase
3. **Performance tracking:** Monitor actual vs. expected signal performance
4. **Continuous optimization:** Refine settings based on real performance data
### Performance Monitoring System
**Signal Quality Tracking:**
- **ELITE Signal Win Rate:** Track highest quality signals separately
- **Component Performance:** Monitor which components provide best signals
- **Regime Performance:** Analyze performance across different market regimes
- **Timeframe Analysis:** Compare performance across different session times
**Mathematical Metric Correlation:**
- **Field Strength vs. Performance:** Higher field strength should correlate with better performance
- **Component Agreement vs. Win Rate:** More component agreement should improve win rates
- **Regime Alignment vs. Success:** Trading with mathematical regime should outperform
### Continuous Optimization Process
**Monthly Review Protocol:**
1. **Performance Analysis:** Review win rates, profit factors, and maximum drawdown
2. **Parameter Assessment:** Evaluate if current settings remain optimal
3. **Market Adaptation:** Adjust for changes in market character or volatility
4. **Component Weighting:** Consider if certain components should receive more/less emphasis
**Quarterly Deep Analysis:**
1. **Mathematical Model Validation:** Verify that mathematical relationships remain valid
2. **Regime Distribution:** Analyze time spent in different market regimes
3. **Signal Evolution:** Track how signal characteristics change over time
4. **Correlation Analysis:** Monitor correlations between different mathematical components
---
## 🌟 UNIQUE INNOVATIONS AND CONTRIBUTIONS
### Revolutionary Mathematical Integration
**First-Ever Implementations:**
1. **Multi-Dimensional Volatility Tensor:** First indicator to implement true tensor analysis for market volatility
2. **Real-Time Hawkes Process:** First trading implementation of self-exciting point processes
3. **Transfer Entropy Trading Signals:** First practical application of information theory for trade generation
4. **Democratic Component Voting:** First algorithmic consensus system for signal generation
5. **Fractal-Projected Signal Quality:** First system to predict signal quality at future price levels
### Advanced Visualization Innovations
**Mathematical Visualization Breakthroughs:**
- **Tensor Field Radiation:** Visual representation of mathematical field energy
- **Dimensional Portal System:** Category theory visualization for regime transitions
- **Information Flow Streams:** Real-time visual display of market information transfer
- **Multi-Layer Fractal Grid:** Intelligent spacing and projection system
- **Regime Intensity Mapping:** Dynamic background showing mathematical regime strength
### Practical Trading Innovations
**Trading System Advances:**
- **Quality-Weighted Signal Generation:** Signals rated by mathematical confidence
- **Regime-Adaptive Strategy Selection:** Automatic strategy optimization based on market personality
- **Anti-Spam Signal Protection:** Mathematical prevention of signal clustering
- **Component Performance Tracking:** Real-time monitoring of algorithmic component success
- **Field-Strength Position Sizing:** Mathematical volatility integration for risk management
---
## ⚖️ RESPONSIBLE USAGE AND LIMITATIONS
### Mathematical Model Limitations
**Understanding Model Boundaries:**
While the TMAE implements sophisticated mathematical concepts, traders must understand fundamental limitations:
- **Markets Are Not Purely Mathematical:** Human psychology, news events, and fundamental factors create unpredictable elements
- **Past Performance Limitations:** Mathematical relationships that worked historically may not persist indefinitely
- **Model Risk:** Complex models can fail during unprecedented market conditions
- **Overfitting Potential:** Highly optimized parameters may not generalize to future market conditions
### Proper Implementation Guidelines
**Risk Management Requirements:**
- **Never Risk More Than 2% Per Trade:** Regardless of signal quality
- **Diversification Mandatory:** Don't rely solely on mathematical signals
- **Position Sizing Discipline:** Use mathematical field strength for sizing, not confidence
- **Stop Loss Non-Negotiable:** Every trade must have predefined risk parameters
**Realistic Expectations:**
- **Mathematical Edge, Not Certainty:** The indicator provides probabilistic advantages, not guaranteed outcomes
- **Learning Curve Required:** Complex mathematical concepts require time to master
- **Market Adaptation Necessary:** Parameters must evolve with changing market conditions
- **Continuous Education Important:** Understanding underlying mathematics improves application
### Ethical Trading Considerations
**Market Impact Awareness:**
- **Information Asymmetry:** Advanced mathematical analysis may provide advantages over other market participants
- **Position Size Responsibility:** Large positions based on mathematical signals can impact market structure
- **Sharing Knowledge:** Consider educational contributions to trading community
- **Fair Market Participation:** Use mathematical advantages responsibly within market framework
### Professional Development Path
**Skill Development Sequence:**
1. **Basic Mathematical Literacy:** Understand fundamental concepts before advanced application
2. **Risk Management Mastery:** Develop disciplined risk control before relying on complex signals
3. **Market Psychology Understanding:** Combine mathematical analysis with behavioral market insights
4. **Continuous Learning:** Stay updated on mathematical finance developments and market evolution
---
## 🔮 CONCLUSION
The Tensor Market Analysis Engine represents a quantum leap forward in technical analysis, successfully bridging the gap between advanced pure mathematics and practical trading applications. By integrating multi-dimensional volatility analysis, fractal market theory, and information flow dynamics, the TMAE reveals market structure invisible to conventional analysis while maintaining visual clarity and practical usability.
### Mathematical Innovation Legacy
This indicator establishes new paradigms in technical analysis:
- **Tensor analysis for market volatility understanding**
- **Stochastic self-excitation for event clustering prediction**
- **Information theory for causality-based trade generation**
- **Democratic algorithmic consensus for signal quality enhancement**
- **Mathematical field visualization for intuitive market understanding**
### Practical Trading Revolution
Beyond mathematical innovation, the TMAE transforms practical trading:
- **Quality-rated signals replace binary buy/sell decisions**
- **Regime-adaptive strategies automatically optimize for market personality**
- **Multi-dimensional risk management integrates mathematical volatility measures**
- **Visual mathematical concepts make complex analysis immediately interpretable**
- **Educational value creates lasting improvement in trading understanding**
### Future-Proof Design
The mathematical foundations ensure lasting relevance:
- **Universal mathematical principles transcend market evolution**
- **Multi-dimensional analysis adapts to new market structures**
- **Regime detection automatically adjusts to changing market personalities**
- **Component democracy allows for future algorithmic additions**
- **Mathematical visualization scales with increasing market complexity**
### Commitment to Excellence
The TMAE represents more than an indicator—it embodies a philosophy of bringing rigorous mathematical analysis to trading while maintaining practical utility and visual elegance. Every component, from the multi-dimensional tensor fields to the democratic signal generation, reflects a commitment to mathematical accuracy, trading practicality, and educational value.
### Trading with Mathematical Precision
In an era where markets grow increasingly complex and computational, the TMAE provides traders with mathematical tools previously available only to institutional quantitative research teams. Yet unlike academic mathematical models, the TMAE translates complex concepts into intuitive visual representations and practical trading signals.
By combining the mathematical rigor of tensor analysis, the statistical power of multi-dimensional volatility modeling, and the information-theoretic insights of transfer entropy, traders gain unprecedented insight into market structure and dynamics.
### Final Perspective
Markets, like nature, exhibit profound mathematical beauty beneath apparent chaos. The Tensor Market Analysis Engine serves as a mathematical lens that reveals this hidden order, transforming how traders perceive and interact with market structure.
Through mathematical precision, visual elegance, and practical utility, the TMAE empowers traders to see beyond the noise and trade with the confidence that comes from understanding the mathematical principles governing market behavior.
Trade with mathematical insight. Trade with the power of tensors. Trade with the TMAE.
*"In mathematics, you don't understand things. You just get used to them." - John von Neumann*
*With the TMAE, mathematical market understanding becomes not just possible, but intuitive.*
— Dskyz, Trade with insight. Trade with anticipation.
RSI-Adaptive T3 [ChartPrime]The RSI-Adaptive T3 is a precision trend-following tool built around the legendary T3 smoothing algorithm developed by Tim Tillson , designed to enhance responsiveness while reducing lag compared to traditional moving averages. Current implementation takes it a step further by dynamically adapting the smoothing length based on real-time RSI conditions — allowing the T3 to “breathe” with market volatility. This dynamic length makes the curve faster in trending moves and smoother during consolidations.
To help traders visualize volatility and directional momentum, adaptive volatility bands are plotted around the T3 line, with visual crossover markers and a dynamic info panel on the chart. It’s ideal for identifying trend shifts, spotting momentum surges, and adapting strategy execution to the pace of the market.
HOIW IT WORKS
At its core, this indicator fuses two ideas:
The T3 Moving Average — a 6-stage recursively smoothed exponential average created by Tim Tillson , designed to reduce lag without sacrificing smoothness. It uses a volume factor to control curvature.
A Dynamic Length Engine — powered by the RSI. When RSI is low (market oversold), the T3 becomes shorter and more reactive. When RSI is high (overbought), the T3 becomes longer and smoother. This creates a feedback loop between price momentum and trend sensitivity.
// Step 1: Adaptive length via RSI
rsi = ta.rsi(src, rsiLen)
rsi_scale = 1 - rsi / 100
len = math.round(minLen + (maxLen - minLen) * rsi_scale)
pine_ema(src, length) =>
alpha = 2 / (length + 1)
sum = 0.0
sum := na(sum ) ? src : alpha * src + (1 - alpha) * nz(sum )
sum
// Step 2: T3 with adaptive length
e1 = pine_ema(src, len)
e2 = pine_ema(e1, len)
e3 = pine_ema(e2, len)
e4 = pine_ema(e3, len)
e5 = pine_ema(e4, len)
e6 = pine_ema(e5, len)
c1 = -v * v * v
c2 = 3 * v * v + 3 * v * v * v
c3 = -6 * v * v - 3 * v - 3 * v * v * v
c4 = 1 + 3 * v + v * v * v + 3 * v * v
t3 = c1 * e6 + c2 * e5 + c3 * e4 + c4 * e3
The result: an evolving trend line that adapts to market tempo in real-time.
KEY FEATURES
⯁ RSI-Based Adaptive Smoothing
The length of the T3 calculation dynamically adjusts between a Min Length and Max Length , based on the current RSI.
When RSI is low → the T3 shortens, tracking reversals faster.
When RSI is high → the T3 stretches, filtering out noise during euphoria phases.
Displayed length is shown in a floating table, colored on a gradient between min/max values.
⯁ T3 Calculation (Tim Tillson Method)
The script uses a 6-stage EMA cascade with a customizable Volume Factor (v) , as designed by Tillson (1998) .
Formula:
T3 = c1 * e6 + c2 * e5 + c3 * e4 + c4 * e3
This technique gives smoother yet faster curves than EMAs or DEMA/Triple EMA.
⯁ Visual Trend Direction & Transitions
The T3 line changes color dynamically:
Color Up (default: blue) → bullish curvature
Color Down (default: orange) → bearish curvature
Plot fill between T3 and delayed T3 creates a gradient ribbon to show momentum expansion/contraction.
Directional shift markers (“🞛”) are plotted when T3 crosses its own delayed value — helping traders spot trend flips or pullback entries.
⯁ Adaptive Volatility Bands
Optional upper/lower bands are plotted around the T3 line using a user-defined volatility window (default: 100).
Bands widen when volatility rises, and contract during compression — similar to Bollinger logic but centered on the adaptive T3.
Shaded band zones help frame breakout setups or mean-reversion zones.
⯁ Dynamic Info Table
A live stats panel shows:
Current adaptive length
Maximum smoothing (▲ MaxLen)
Minimum smoothing (▼ MinLen)
All values update in real time and are color-coded to match trend direction.
HOW TO USE
Use T3 crossovers to detect trend transitions, especially during periods of volatility compression.
Watch for volatility contraction in the bands — breakouts from narrow band periods often precede trend bursts.
The adaptive smoothing length can also be used to assess current market tempo — tighter = faster; wider = slower.
CONCLUSION
RSI-Adaptive T3 modernizes one of the most elegant smoothing algorithms in technical analysis with intelligent RSI responsiveness and built-in volatility bands. It gives traders a cleaner read on trend health, directional shifts, and expansion dynamics — all in a visually efficient package. Perfect for scalpers, swing traders, and algorithmic modelers alike, it delivers advanced logic in a plug-and-play format.
[blackcat] L2 Multi-Level Price Condition TrackerOVERVIEW
The L2 Multi-Level Price Condition Tracker represents an innovative approach to analyzing financial markets by simultaneously monitoring multiple price levels, thus providing traders with a holistic view of market dynamics. By combining dynamic calculations based on moving averages and price deviations, this tool aims to deliver precise and actionable insights into potential entry and exit points. It leverages sophisticated statistical measures to identify key thresholds that signify shifts in market sentiment, thereby aiding traders in making well-informed decisions. 🎯
Key benefits encompass:
• Comprehensive calculation of midpoints and average prices indicating short-term trend directions.
• Interactive visualization elements enhancing interpretability effortlessly.
• Real-time generation of buy/sell signals driven by precise condition evaluations.
TECHNICAL ANALYSIS COMPONENTS
📉 Midpoint Calculations:
Computes central reference points derived from high-low ranges establishing baseline supports/resistances.
Utilizes Simple Moving Averages (SMAs) along with standardized deviation formulas smoothing out volatility while preserving long-term trends accurately.
Facilitates identification of directional biases reflecting underlying market forces dynamically.
🕵️♂️ Advanced Price Level Detection:
Derives upper/lower bounds adjusting sensitivities adaptively responding to changing conditions flexibly.
Employs proprietary logic distinguishing between bullish/bearish sentiments promptly signaling transitions effectively.
Ensures consistent adherence to predefined statistical protocols maintaining accuracy robustly.
🎥 Dynamic Signal Generation:
Detects crossovers indicating dominance shifts between buyers/sellers promptly triggering timely alerts.
Integrates conditional logic reinforcing signal validity minimizing erroneous activations systematically.
Supports adaptive thresholds tuning sensitivities based on evolving market conditions flexibly accommodating varying scenarios.
INDICATOR FUNCTIONALITY
🔢 Core Algorithms:
Utilizes moving averages alongside standardized deviation formulas generating precise net volume measurements.
Implements Arithmetic Mean Line Algorithm (AMLA) smoothing techniques improving interpretability.
Ensures consistent alignment with established statistical principles preserving fidelity.
🖱️ User Interface Elements:
Dedicated plots displaying real-time midpoint markers facilitating swift decision-making.
Context-sensitive color coding distinguishing positive/negative deviations intuitively highlighting key activations clearly.
Background shading emphasizing proximity to crucial threshold activations enhancing visibility focusing attention on vital signals promptly.
STRATEGY IMPLEMENTATION
✅ Entry Conditions:
Confirm bullish/bearish setups validated through multiple confirmatory signals assessing concurrent market sentiment factors.
Validate entry decisions considering alignment between calculated midpoints and broader trend directions ensuring coherence.
Monitor cumulative breaches signifying potential trend reversals executing partial/total closes contingent upon predetermined loss limits preserving capital efficiently.
🚫 Exit Mechanisms:
Trigger exits upon hitting predefined thresholds derived from historical analyses promptly executing closures.
Execute partial/total closes contingent upon cumulative loss limits preserving capital efficiently managing exposures prudently.
Conduct periodic reviews gauging strategy effectiveness rigorously identifying areas needing refinement implementing corrective actions iteratively enhancing performance metrics steadily.
PARAMETER CONFIGURATIONS
🎯 Optimization Guidelines:
Lookback Period: Governs responsiveness versus stability balancing sensitivity/stability governing moving averages aligning with preferred granularity.
Price Source: Dictates primary data series driving volume calculations selecting relevant inputs accurately tailoring strategies accordingly.
💬 Customization Recommendations:
Commence with baseline defaults; iteratively refine parameters isolating individual impacts evaluating adjustments independently prior to combined modifications minimizing disruptions.
Prioritize minimizing erroneous trigger occurrences first optimizing signal fidelity sustaining balanced risk-reward profiles irrespective of chosen settings upholding disciplined approaches preserving capital efficiently.
ADVANCED RISK MANAGEMENT
🛡️ Proactive Risk Mitigation Techniques:
Enforce strict compliance with pre-defined maximum leverage constraints adhering strictly to guidelines managing exposures prudently.
Mandatorily apply trailing stop-loss orders conforming to script outputs enforcing discipline rigorously preventing adverse consequences.
Allocate positions proportionately relative to available capital reserves conducting periodic reviews gauging effectiveness continuously identifying improvement opportunities steadily.
⚠️ Potential Pitfalls & Solutions:
Address frequent violations arising during heightened volatility phases necessitating manual interventions judiciously preparing contingency plans proactively mitigating risks effectively.
Manage false alerts warranting immediate attention avoiding adverse consequences systematically implementing corrective actions reliably.
Prepare proactive responses amid adverse movements ensuring seamless functionality amidst fluctuating conditions fortifying resilience against anomalies robustly.
PERFORMANCE MONITORING METRICS
🔍 Evaluation Criteria:
Assess win percentages consistently across diverse trading instruments gauging reliability measuring profitability efficiency accurately evaluating downside risks comprehensively uncovering systematic biases potentially skewing outcomes.
Calculate average profit ratios per successful execution benchmarking actual vs expected performances documenting results meticulously tracking progress dynamically addressing identified shortcomings proactively fostering continuous improvements.
📈 Historical Data Analysis Tools:
Maintain detailed logs capturing every triggered event recording realized profits/losses comparing simulated projections accurately identifying discrepancies warranting investigation implementing iterative refinements steadily enhancing performance metrics progressively.
Identify recurrent systematic errors demanding corrective actions implementing iterative refinements steadily addressing identified shortcomings proactively fostering continuous enhancements dynamically improving robustness resiliently.
PROBLEM SOLVING ADVICE
🔧 Frequent Encountered Challenges:
Unpredictable behaviors emerging within thinly traded markets requiring filtration processes enhancing signal integrity excluding low-liquidity assets prone to erratic movements effectively.
Latency issues manifesting during abrupt price fluctuations causing missed opportunities introducing buffer intervals safeguarding major news/event impacts mitigating distortions seamlessly verifying reliable connections ensuring uninterrupted data flows guaranteeing accurate interpretations dependably.
💡 Effective Resolution Pathways:
Limit ongoing optimization attempts preventing model degradation maintaining optimal performance levels consistently recalibrating parameters periodically adapting strategies flexibly responding appropriately amidst varying conditions dynamically improving robustness resiliently.
Verify reliable connections ensuring uninterrupted data flows guaranteeing accurate interpretations dependably bolstering overall efficacy systematically addressing identified shortcomings dynamically fostering continuous advancements.
THANKS
Heartfelt acknowledgment extends to all developers contributing invaluable insights regarding multi-level price condition-based trading methodologies! ✨
[blackcat] L2 Z-Score of PriceOVERVIEW
The L2 Z-Score of Price indicator offers traders an insightful perspective into how current prices diverge from their historical norms through advanced statistical measures. By leveraging Z-scores, it provides a robust framework for identifying potential reversals in financial markets. The Z-score quantifies the number of standard deviations that a data point lies away from the mean, thus serving as a critical metric for recognizing overbought or oversold conditions. 🎯
Key benefits encompass:
• Precise calculation of Z-scores reflecting true price deviations.
• Interactive plotting features enhancing visual clarity.
• Real-time generation of buy/sell signals based on crossover events.
STATISTICAL ANALYSIS COMPONENTS
📉 Mean Calculation:
Utilizes Simple Moving Averages (SMAs) to establish baseline price references.
Provides smooth representations filtering short-term noise preserving long-term trends.
Fundamental for deriving subsequent deviation metrics accurately.
📈 Standard Deviation Measurement:
Quantifies dispersion around established means revealing underlying variability.
Crucial for assessing potential volatility levels dynamically adapting strategies accordingly.
Facilitates precise Z-score derivations ensuring statistical rigor.
🕵️♂️ Z-SCORE DETECTION:
Measures standardized distances indicating relative positions within distributions.
Helps pinpoint extreme conditions signaling impending reversals proactively.
Enables early identification of trend exhaustion phases prompting timely actions.
INDICATOR FUNCTIONALITY
🔢 Core Algorithms:
Integrates SMAs along with standardized deviation formulas generating precise Z-scores.
Employs Arithmetic Mean Line Algorithm (AMLA) smoothing techniques improving interpretability.
Ensures consistent adherence to predefined statistical protocols maintaining accuracy.
🖱️ User Interface Elements:
Dedicated plots displaying real-time Z-score markers facilitating swift decision-making.
Context-sensitive color coding distinguishing positive/negative deviations intuitively.
Background shading highlighting proximity to key threshold activations enhancing visibility.
STRATEGY IMPLEMENTATION
✅ Entry Conditions:
Confirm bullish/bearish setups validated through multiple confirmatory signals.
Validate entry decisions considering concurrent market sentiment factors.
Assess alignment between Z-score readings and broader trend directions ensuring coherence.
🚫 Exit Mechanisms:
Trigger exits upon hitting predetermined thresholds derived from historical analyses.
Monitor continuous breaches signifying potential trend reversals promptly executing closures.
Execute partial/total closes contingent upon cumulative loss limits preserving capital efficiently.
PARAMETER CONFIGURATIONS
🎯 Optimization Guidelines:
Length: Governs responsiveness versus smoothing trade-offs balancing sensitivity/stability.
Price Source: Dictates primary data series driving Z-score computations selecting relevant inputs accurately.
💬 Customization Recommendations:
Commence with baseline defaults; iteratively refine parameters isolating individual impacts.
Evaluate adjustments independently prior to combined modifications minimizing disruptions.
Prioritize minimizing erroneous trigger occurrences first optimizing signal fidelity.
Sustain balanced risk-reward profiles irrespective of chosen settings upholding disciplined approaches.
ADVANCED RISK MANAGEMENT
🛡️ Proactive Risk Mitigation Techniques:
Enforce strict compliance with pre-defined maximum leverage constraints adhering strictly to guidelines.
Mandatorily apply trailing stop-loss orders conforming to script outputs reinforcing discipline.
Allocate positions proportionately relative to available capital reserves managing exposures prudently.
Conduct periodic reviews gauging strategy effectiveness rigorously identifying areas needing refinement.
⚠️ Potential Pitfalls & Solutions:
Address frequent violations arising during heightened volatility phases necessitating manual interventions judiciously.
Manage false alerts warranting immediate attention avoiding adverse consequences systematically.
Prepare contingency plans mitigating margin call possibilities preparing proactive responses effectively.
Continuously assess automated system reliability amidst fluctuating conditions ensuring seamless functionality.
PERFORMANCE AUDITS & REFINEMENTS
🔍 Critical Evaluation Metrics:
Assess win percentages consistently across diverse trading instruments gauging reliability.
Calculate average profit ratios per successful execution measuring profitability efficiency accurately.
Measure peak drawdown durations alongside associated magnitudes evaluating downside risks comprehensively.
Analyze signal generation frequencies revealing hidden patterns potentially skewing outcomes uncovering systematic biases.
📈 Historical Data Analysis Tools:
Maintain comprehensive records capturing every triggered event meticulously documenting results.
Compare realized profits/losses against backtested simulations benchmarking actual vs expected performances accurately.
Identify recurrent systematic errors demanding corrective actions implementing iterative refinements steadily.
Document evolving performance metrics tracking progress dynamically addressing identified shortcomings proactively.
PROBLEM SOLVING ADVICE
🔧 Frequent Encountered Challenges:
Unpredictable behaviors emerging within thinly traded markets requiring filtration processes.
Latency issues manifesting during abrupt price fluctuations causing missed opportunities.
Overfitted models yielding suboptimal results post-extensive tuning demanding recalibrations.
Inaccuracies stemming from incomplete/inaccurate data feeds necessitating verification procedures.
💡 Effective Resolution Pathways:
Exclude low-liquidity assets prone to erratic movements enhancing signal integrity.
Introduce buffer intervals safeguarding major news/event impacts mitigating distortions effectively.
Limit ongoing optimization attempts preventing model degradation maintaining optimal performance levels consistently.
Verify reliable connections ensuring uninterrupted data flows guaranteeing accurate interpretations reliably.
USER ENGAGEMENT SEGMENT
🤝 Community Contributions Welcome
Highly encourage active participation sharing experiences & recommendations!
[blackcat] L3 Smart Money FlowCOMPREHENSIVE ANALYSIS OF THE L3 SMART MONEY FLOW INDICATOR
🌐 OVERVIEW:
The L3 Smart Money Flow indicator represents a sophisticated multi-dimensional analytics tool combining traditional momentum measurements with advanced institutional investor tracking capabilities. It's particularly effective at identifying large-scale capital movement dynamics that often precede significant price shifts.
Core Objectives:
• Detect subtle but meaningful price action anomalies indicating major player involvement
• Provide clear entry/exit markers based on multiple validated criteria
• Offer risk-managed positioning strategies suitable for various account sizes
• Maintain operational efficiency even during high volatility regimes
THEORETICAL BACKDROP AND METHODOLOGY
🎓 Conceptual Foundation Principles:
Utilizes Time-Varying Moving Averages (TVMA) responding adaptively to changing market states
Implements Extended Smoothing Algorithm (XSA) providing enhanced filtration characteristics
Employs asymmetric weight distribution favoring recent price observations over historical ones
→ Analyzes price-weighted closing prices incorporating volume influence indirectly
← Applies Asymmetric Local Maximum (ALMA) filters generating institution-specific trends
⟸ Combines multiple temporal perspectives producing robust directional assessments
✓ Calculates normalized momentum ratios comparing current state against extended range extremes
✗ Filters out insignificant fluctuations via double-stage verification process
⤾ Generates actionable alerts upon exceeding predefined significance boundaries
CONFIGURABLE PARAMETERS IN DEPTH
⚙️ Input Customization Options Detailed Explanation:
Temporal Resolution Control:
→ TVMA Length Setting:
Minimum value constraint ensuring mathematical validity
Higher numbers increase smoothing effect reducing reaction velocity
Lower intervals enhance responsiveness potentially increasing noise exposure
Validation Threshold Definition:
↓ Bull-Bear Boundary Level:
Establishes fundamental acceptance/rejection zones
Typically set near extreme values reflecting rare occurrence probability
Can be adjusted per instrument liquidity profiles if necessary
ADVANCED ALGORITHMIC PROCEDURES BREAKDOWN
💻 Internal Operation Architecture:
Base Calculations Infrastructure:
☑ Raw Data Preparation and Normalization
☐ High/Low/Closing Aggregation Processes
☒ Range Estimation Algorithms
Intermediate Transform Engine:
📈 Momentum Ratio Computation Workflow
↔ First Pass XSA Application Details
➖ Second Stage Refinement Mechanics
Final Output Synthesis Framework:
➢ Composite Reading Compilation Logic
➣ Validation Status Determination Process
➤ Alert Trigger Decision Making Structure
INTERACTIVE VISUAL INTERFACE COMPONENTS
🎨 User Experience Interface Elements:
🔵 Plotting Series Hierarchy:
→ Primary FundFlow Signal: White trace marking core oscillator progression
↑ Secondary Confirmation Overlay: Orange/Yellow highlighting validation status
🟥 Risk/Reward Boundaries: Aqua line delineating strategic areas requiring attention
🏷️ Interactive Marker System:
✔ "BUY": Green upward-pointing labels denoting confirmed long entries
❌ "SELL": Red downward-facing badges signaling short setups
PRACTICAL APPLICATION STRATEGY GUIDE
📋 Operational Deployment Instructions:
Strategic Planning Initiatives:
• Define precise profit targets considering realistic reward/risk scenarios
→ Set maximum acceptable loss thresholds protecting available resources adequately
↓ Develop contingency plans addressing unexpected adverse developments promptly
Live Trading Engagement Protocols:
→ Maintaining vigilant monitoring of label placement activities continuously
↓ Tracking order fill success rates across implemented grids regularly
↑ Evaluating system effectiveness compared alternative methodologies periodically
Performance Optimization Techniques:
✔ Implement incremental improvements iteratively throughout lifecycle
❌ Eliminate ineffective component variations systematically
⟹ Ensure proportional growth capability matching user needs appropriately
EFFICIENCY ENHANCEMENT APPROACHES
🚀 Ongoing Development Strategy:
Resource Management Focus Areas:
→ Minimizing redundant computation cycles through intelligent caching mechanisms
↓ Leveraging parallel processing capabilities where feasible efficiently
↑ Optimizing storage access patterns improving response times substantially
Scalability Consideration Factors:
✔ Adapting to varying account sizes/market capitalizations seamlessly
❌ Preventing bottlenecks limiting concurrent operation capacity
⟹ Ensuring balanced growth capability matching evolving requirements accurately
Maintenance Routine Establishment:
✓ Regular codebase updates incorporation keeping functionality current
↓ Periodic performance audits conducting verifying continued effectiveness
↑ Documentation refinement updating explaining any material modifications made
SYSTEMATIC RISK CONTROL MECHANISMS
🛡️ Comprehensive Protection Systems:
Position Sizing Governance:
∅ Never exceed predetermined exposure limitations strictly observed
± Scale entries proportionally according to available resources carefully
× Include slippage allowances within planning stages realistically
Emergency Response Procedures:
↩ Well-defined exit strategies including trailing stops activation logic
🌀 Contingency plan formulation covering worst-case scenario contingencies
⇄ Recovery procedure documentation outlining restoration steps methodically
EXODUS EXODUS by (DAFE) Trading Systems
EXODUS is a sophisticated trading algorithm built by Dskyz (DAFE) Trading Systems for competitive and competition purposes, designed to identify high-probability trades with robust risk management. this strategy leverages a multi-signal voting system, combining three core components—SPR, VWMO, and VEI—alongside ADX, choppiness filters, and ATR-based volatility gates to ensure trades are taken only in favorable market conditions. the algo uses a take-profit to stop-loss ratio, dynamic position sizing, and a strict voting mechanism requiring all signals to align before entering a trade.
EXODUS was not overfitted for any specific symbol. instead, it uses a generic tuned setting, making it versatile across various markets. while it can trade futures, it’s not currently set up for it but has the potential to do more with further development. visuals are intentionally minimal due to its competition focus, prioritizing performance over aesthetics. a more visually stunning version may be released in the future with enhanced graphics.
The Unique Core Components Developed for EXODUS
SPR (Session Price Recalibration)
SPR measures momentum during regular trading hours (RTH, 0930-1600, America/New_York) to catch session-specific trends.
spr_lookback = input.int(15, "SPR Lookback") this sets how many bars back SPR looks to calculate momentum (default 15 bars). it compares the current session’s price-volume score to the score 15 bars ago to gauge momentum strength.
how it works: a longer lookback smooths out the signal, focusing on bigger trends. a shorter one makes SPR more sensitive to recent moves.
how to adjust: on a 1-hour chart, 15 bars is 15 hours (about 2 trading days). if you’re on a shorter timeframe like 5 minutes, 15 bars is just 75 minutes, so you might want to increase it to 50 or 100 to capture more meaningful trends. if you’re trading a choppy stock, a shorter lookback (like 5) can help catch quick moves, but it might give more false signals.
spr_threshold = input.float (0.7, "SPR Threshold")
this is the cutoff for SPR to vote for a trade (default 0.7). if SPR’s normalized value is above 0.7, it votes for a long; below -0.7, it votes for a short.
how it works: SPR normalizes its momentum score by ATR, so this threshold ensures only strong moves count. a higher threshold means fewer trades but higher conviction.
how to adjust: if you’re getting too few trades, lower it to 0.5 to let more signals through. if you’re seeing too many false entries, raise it to 1.0 for stricter filtering. test on your chart to find a balance.
spr_atr_length = input.int(21, "SPR ATR Length") this sets the ATR period (default 21 bars) used to normalize SPR’s momentum score. ATR measures volatility, so this makes SPR’s signal relative to market conditions.
how it works: a longer ATR period (like 21) smooths out volatility, making SPR less jumpy. a shorter one makes it more reactive.
how to adjust: if you’re trading a volatile stock like TSLA, a longer period (30 or 50) can help avoid noise. for a calmer stock, try 10 to make SPR more responsive. match this to your timeframe—shorter timeframes might need a shorter ATR.
rth_session = input.session("0930-1600","SPR: RTH Sess.") rth_timezone = "America/New_York" this defines the session SPR uses (0930-1600, New York time). SPR only calculates momentum during these hours to focus on RTH activity.
how it works: it ignores pre-market or after-hours noise, ensuring SPR captures the main market action.
how to adjust: if you trade a different session (like London hours, 0300-1200 EST), change the session to match. you can also adjust the timezone if you’re in a different region, like "Europe/London". just make sure your chart’s timezone aligns with this setting.
VWMO (Volume-Weighted Momentum Oscillator)
VWMO measures momentum weighted by volume to spot sustained, high-conviction moves.
vwmo_momlen = input.int(21, "VWMO Momentum Length") this sets how many bars back VWMO looks to calculate price momentum (default 21 bars). it takes the price change (close minus close 21 bars ago).
how it works: a longer period captures bigger trends, while a shorter one reacts to recent swings.
how to adjust: on a daily chart, 21 bars is about a month—good for trend trading. on a 5-minute chart, it’s just 105 minutes, so you might bump it to 50 or 100 for more meaningful moves. if you want faster signals, drop it to 10, but expect more noise.
vwmo_volback = input.int(30, "VWMO Volume Lookback") this sets the period for calculating average volume (default 30 bars). VWMO weights momentum by volume divided by this average.
how it works: it compares current volume to the average to see if a move has strong participation. a longer lookback smooths the average, while a shorter one makes it more sensitive.
how to adjust: for stocks with spiky volume (like NVDA on earnings), a longer lookback (50 or 100) avoids overreacting to one-off spikes. for steady volume stocks, try 20. match this to your timeframe—shorter timeframes might need a shorter lookback.
vwmo_smooth = input.int(9, "VWMO Smoothing")
this sets the SMA period to smooth VWMO’s raw momentum (default 9 bars).
how it works: smoothing reduces noise in the signal, making VWMO more reliable for voting. a longer smoothing period cuts more noise but adds lag.
how to adjust: if VWMO is too jumpy (lots of false votes), increase to 15. if it’s too slow and missing trades, drop to 5. test on your chart to see what keeps the signal clean but responsive.
vwmo_threshold = input.float(10, "VWMO Threshold") this is the cutoff for VWMO to vote for a trade (default 10). above 10, it votes for a long; below -10, a short.
how it works: it ensures only strong momentum signals count. a higher threshold means fewer but stronger trades.
how to adjust: if you want more trades, lower it to 5. if you’re getting too many weak signals, raise it to 15. this depends on your market—volatile stocks might need a higher threshold to filter noise.
VEI (Velocity Efficiency Index)
VEI measures market efficiency and velocity to filter out choppy moves and focus on strong trends.
vei_eflen = input.int(14, "VEI Efficiency Smoothing") this sets the EMA period for smoothing VEI’s efficiency calc (bar range / volume, default 14 bars).
how it works: efficiency is how much price moves per unit of volume. smoothing it with an EMA reduces noise, focusing on consistent efficiency. a longer period smooths more but adds lag.
how to adjust: for choppy markets, increase to 20 to filter out noise. for faster markets, drop to 10 for quicker signals. this should match your timeframe—shorter timeframes might need a shorter period.
vei_momlen = input.int(8, "VEI Momentum Length") this sets how many bars back VEI looks to calculate momentum in efficiency (default 8 bars).
how it works: it measures the change in smoothed efficiency over 8 bars, then adjusts for inertia (volume-to-range). a longer period captures bigger shifts, while a shorter one reacts faster.
how to adjust: if VEI is missing quick reversals, drop to 5. if it’s too noisy, raise to 12. test on your chart to see what catches the right moves without too many false signals.
vei_threshold = input.float(4.5, "VEI Threshold") this is the cutoff for VEI to vote for a trade (default 4.5). above 4.5, it votes for a long; below -4.5, a short.
how it works: it ensures only strong, efficient moves count. a higher threshold means fewer trades but higher quality.
how to adjust: if you’re not getting enough trades, lower to 3. if you’re seeing too many false entries, raise to 6. this depends on your market—fast stocks like NQ1 might need a lower threshold.
Features
Multi-Signal Voting: requires all three signals (SPR, VWMO, VEI) to align for a trade, ensuring high-probability setups.
Risk Management: uses ATR-based stops (2.1x) and take-profits (4.1x), with dynamic position sizing based on a risk percentage (default 0.4%).
Market Filters: ADX (default 27) ensures trending conditions, choppiness index (default 54.5) avoids sideways markets, and ATR expansion (default 1.12) confirms volatility.
Dashboard: provides real-time stats like SPR, VWMO, VEI values, net P/L, win rate, and streak, with a clean, functional design.
Visuals
EXODUS prioritizes performance over visuals, as it was built for competitive and competition purposes. entry/exit signals are marked with simple labels and shapes, and a basic heatmap highlights market regimes. a more visually stunning update may be released later, with enhanced graphics and overlays.
Usage
EXODUS is designed for stocks and ETFs but can be adapted for futures with adjustments. it performs best in trending markets with sufficient volatility, as confirmed by its generic tuning across symbols like TSLA, AMD, NVDA, and NQ1. adjust inputs like SPR threshold, VWMO smoothing, or VEI momentum length to suit specific assets or timeframes.
Setting I used: (Again, these are a generic setting, each security needs to be fine tuned)
SPR LB = 19 SPR TH = 0.5 SPR ATR L= 21 SPR RTH Sess: 9:30 – 16:00
VWMO L = 21 VWMO LB = 18 VWMO S = 6 VWMO T = 8
VEI ES = 14 VEI ML = 21 VEI T = 4
R % = 0.4
ATR L = 21 ATR M (S) =1.1 TP Multi = 2.1 ATR min mult = 0.8 ATR Expansion = 1.02
ADX L = 21 Min ADX = 25
Choppiness Index = 14 Chop. Max T = 55.5
Backtesting: TSLA
Frame: Jan 02, 2018, 08:00 — May 01, 2025, 09:00
Slippage: 3
Commission .01
Disclaimer
this strategy is for educational purposes. past performance is not indicative of future results. trading involves significant risk, and you should only trade with capital you can afford to lose. always backtest and validate any strategy before using it in live markets.
(This publishing will most likely be taken down do to some miscellaneous rule about properly displaying charting symbols, or whatever. Once I've identified what part of the publishing they want to pick on, I'll adjust and repost.)
About the Author
Dskyz (DAFE) Trading Systems is dedicated to building high-performance trading algorithms. EXODUS is a product of rigorous research and development, aimed at delivering consistent, and data-driven trading solutions.
Use it with discipline. Use it with clarity. Trade smarter.
**I will continue to release incredible strategies and indicators until I turn this into a brand or until someone offers me a contract.
2025 Created by Dskyz, powered by DAFE Trading Systems. Trade smart, trade bold.
Finite Difference - Backward (mcbw_)In calculus there exists a 'derivative', which simply just measures the difference between two points on a curve. For well behaved mathematical functions there are infinitely many points and so there exists a derivative at every point. Where there are infinitely many points in a curve that curve is called 'continuous'. Continuous curves are very nice to deal with since each point on it exists almost exactly where its neighbors are. However, if the curve does not have infinitely many points on it, but instead has a finite number of points on it, that curve is called 'discrete' instead of continuous. Taking the derivative of discrete curves is much trickier business since there are none of the mathematical conveniences that a continuous offers. In the real world everything we measure is a discrete curve, including Price (since we measure it a finite number of times, aka each candlestick)!
The branch of Discrete Mathematics has found an approach to measure the derivative along a discrete curve, that approach is aptly called " Finite Difference ". To get a more accurate approximation of a discrete derivative, the finite difference approach uses weighted combinations of neighboring points. The most common type of finite difference is a 'central' difference, this uses a combination of points before and after the point of interest to approximate the discrete derivative. This is great for historical analysis but is not of much use for trading algorithms since it technically means using future prices to calculate the derivative of the current point. Instead we can use a less common variant called a ' Backwards Difference ' that only uses a combination of points before the current one to help approximate the current derivative.
In this script you can choose the " Order " of your derivative and the " Accuracy " of its approximation. This script is for educational purposes for folks building trading algorithms. Many trading algorithms often have an element of seeing how much Price has changed from the previous candle to the current candle. This approach is the lowest accuracy derivative possible, and using the backwards finite differences, made available for the first time on TradingView (!!), algorithms that use derivatives can now have higher orders of accuracy!
Happy Trading/Developing!
AiTrend Pattern Matrix for kNN Forecasting (AiBitcoinTrend)The AiTrend Pattern Matrix for kNN Forecasting (AiBitcoinTrend) is a cutting-edge indicator that combines advanced mathematical modeling, AI-driven analytics, and segment-based pattern recognition to forecast price movements with precision. This tool is designed to provide traders with deep insights into market dynamics by leveraging multivariate pattern detection and sophisticated predictive algorithms.
👽 Core Features
Segment-Based Pattern Recognition
At its heart, the indicator divides price data into discrete segments, capturing key elements like candle bodies, high-low ranges, and wicks. These segments are normalized using ATR-based volatility adjustments to ensure robustness across varying market conditions.
AI-Powered k-Nearest Neighbors (kNN) Prediction
The predictive engine uses the kNN algorithm to identify the closest historical patterns in a multivariate dictionary. By calculating the distance between current and historical segments, the algorithm determines the most likely outcomes, weighting predictions based on either proximity (distance) or averages.
Dynamic Dictionary of Historical Patterns
The indicator maintains a rolling dictionary of historical patterns, storing multivariate data for:
Candle body ranges, High-low ranges, Wick highs and lows.
This dynamic approach ensures the model adapts continuously to evolving market conditions.
Volatility-Normalized Forecasting
Using ATR bands, the indicator normalizes patterns, reducing noise and enhancing the reliability of predictions in high-volatility environments.
AI-Driven Trend Detection
The indicator not only predicts price levels but also identifies market regimes by comparing current conditions to historically significant highs, lows, and midpoints. This allows for clear visualizations of trend shifts and momentum changes.
👽 Deep Dive into the Core Mathematics
👾 Segment-Based Multivariate Pattern Analysis
The indicator analyzes price data by dividing each bar into distinct segments, isolating key components such as:
Body Ranges: Differences between the open and close prices.
High-Low Ranges: Capturing the full volatility of a bar.
Wick Extremes: Quantifying deviations beyond the body, both above and below.
Each segment contributes uniquely to the predictive model, ensuring a rich, multidimensional understanding of price action. These segments are stored in a rolling dictionary of patterns, enabling the indicator to reference historical behavior dynamically.
👾 Volatility Normalization Using ATR
To ensure robustness across varying market conditions, the indicator normalizes patterns using Average True Range (ATR). This process scales each component to account for the prevailing market volatility, allowing the algorithm to compare patterns on a level playing field regardless of differing price scales or fluctuations.
👾 k-Nearest Neighbors (kNN) Algorithm
The AI core employs the kNN algorithm, a machine-learning technique that evaluates the similarity between the current pattern and a library of historical patterns.
Euclidean Distance Calculation:
The indicator computes the multivariate distance across four distinct dimensions: body range, high-low range, wick low, and wick high. This ensures a comprehensive and precise comparison between patterns.
Weighting Schemes: The contribution of each pattern to the forecast is either weighted by its proximity (distance) or averaged, based on user settings.
👾 Prediction Horizon and Refinement
The indicator forecasts future price movements (Y_hat) by predicting logarithmic changes in the price and projecting them forward using exponential scaling. This forecast is smoothed using a user-defined EMA filter to reduce noise and enhance actionable clarity.
👽 AI-Driven Pattern Recognition
Dynamic Dictionary of Patterns: The indicator maintains a rolling dictionary of N multivariate patterns, continuously updated to reflect the latest market data. This ensures it adapts seamlessly to changing market conditions.
Nearest Neighbor Matching: At each bar, the algorithm identifies the most similar historical pattern. The prediction is based on the aggregated outcomes of the closest neighbors, providing confidence levels and directional bias.
Multivariate Synthesis: By combining multiple dimensions of price action into a unified prediction, the indicator achieves a level of depth and accuracy unattainable by single-variable models.
Visual Outputs
Forecast Line (Y_hat_line):
A smoothed projection of the expected price trend, based on the weighted contribution of similar historical patterns.
Trend Regime Bands:
Dynamic high, low, and midlines highlight the current market regime, providing actionable insights into momentum and range.
Historical Pattern Matching:
The nearest historical pattern is displayed, allowing traders to visualize similarities
👽 Applications
Trend Identification:
Detect and follow emerging trends early using dynamic trend regime analysis.
Reversal Signals:
Anticipate market reversals with high-confidence predictions based on historically similar scenarios.
Range and Momentum Trading:
Leverage multivariate analysis to understand price ranges and momentum, making it suitable for both breakout and mean-reversion strategies.
Disclaimer: This information is for entertainment purposes only and does not constitute financial advice. Please consult with a qualified financial advisor before making any investment decisions.
Bayesian Price Projection Model [Pinescriptlabs]📊 Dynamic Price Projection Algorithm 📈
This algorithm combines **statistical calculations**, **technical analysis**, and **Bayesian theory** to forecast a future price while providing **uncertainty ranges** that represent upper and lower bounds. The calculations are designed to adjust projections by considering market **trends**, **volatility**, and the historical probabilities of reaching new highs or lows.
Here’s how it works:
🚀 Future Price Projection
A dynamic calculation estimates the future price based on three key elements:
1. **Trend**: Defines whether the market is predisposed to move up or down.
2. **Volatility**: Quantifies the magnitude of the expected change based on historical fluctuations.
3. **Time Factor**: Uses the logarithm of the projected period (`proyeccion_dias`) to adjust how time impacts the estimate.
🧠 **Bayesian Probabilistic Adjustment**
- Conditional probabilities are calculated using **Bayes' formula**:
\
This models future events using conditional information:
- **Probability of reaching a new all-time high** if the price is trending upward.
- **Probability of reaching a new all-time low** if the price is trending downward.
- These probabilities refine the future price estimate by considering:
- **Higher volatility** increases the likelihood of hitting extreme levels (highs/lows).
- **Market trends** influence the expected price movement direction.
🌟 **Volatility Calculation**
- Volatility is measured using the **ATR (Average True Range)** indicator with a 14-period window. This reflects the average amplitude of price fluctuations.
- To express volatility as a percentage, the ATR is normalized by dividing it by the closing price and multiplying it by 200.
- Volatility is then categorized into descriptive levels (e.g., **Very Low**, **Low**, **Moderate**, etc.) for better interpretation.
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🎯 **Deviation Limits (Upper and Lower)**
- The upper and lower limits form a **projected range** around the estimated future price, providing a framework for uncertainty.
- These limits are calculated by adjusting the ATR using:
- A user-defined **multiplier** (`factor_desviacion`).
- **Bayesian probabilities** calculated earlier.
- The **square root of the projected period** (`proyeccion_dias`), incorporating the principle that uncertainty grows over time.
🔍 **Interpreting the Model**
This can be seen as a **dynamic probabilistic model** that:
- Combines **technical analysis** (trends and ATR).
- Refines probabilities using **Bayesian theory**.
- Provides a **visual projection range** to help you understand potential future price movements and associated uncertainties.
⚡ Whether you're analyzing **volatile markets** or confirming **bullish/bearish scenarios**, this tool equips you with a robust, data-driven approach! 🚀
Español :
📊 Algoritmo de Proyección de Precio Dinámico 📈
Este algoritmo combina **cálculos estadísticos**, **análisis técnico** y **la teoría de Bayes** para proyectar un precio futuro, junto con rangos de **incertidumbre** que representan los límites superior e inferior. Los cálculos están diseñados para ajustar las proyecciones considerando la **tendencia del mercado**, **volatilidad** y las probabilidades históricas de alcanzar nuevos máximos o mínimos.
Aquí se explica su funcionamiento:
🚀 **Proyección de Precio Futuro**
Se realiza un cálculo dinámico del precio futuro estimado basado en tres elementos clave:
1. **Tendencia**: Define si el mercado tiene predisposición a subir o bajar.
2. **Volatilidad**: Determina la magnitud del cambio esperado en función de las fluctuaciones históricas.
3. **Factor de Tiempo**: Usa el logaritmo del período proyectado (`proyeccion_dias`) para ajustar cómo el tiempo afecta la estimación.
🧠 **Ajuste Probabilístico con la Teoría de Bayes**
- Se calculan probabilidades condicionales mediante la fórmula de **Bayes**:
\
Esto permite modelar eventos futuros considerando información condicional:
- **Probabilidad de alcanzar un nuevo máximo histórico** si el precio sube.
- **Probabilidad de alcanzar un nuevo mínimo histórico** si el precio baja.
- Estas probabilidades ajustan la estimación del precio futuro considerando:
- **Mayor volatilidad** aumenta la probabilidad de alcanzar niveles extremos (máximos/mínimos).
- **La tendencia del mercado** afecta la dirección esperada del movimiento del precio.
🌟 **Cálculo de Volatilidad**
- La volatilidad se mide usando el indicador **ATR (Average True Range)** con un período de 14 velas. Este indicador refleja la amplitud promedio de las fluctuaciones del precio.
- Para obtener un valor porcentual, el ATR se normaliza dividiéndolo por el precio de cierre y multiplicándolo por 200.
- Además, se clasifica esta volatilidad en categorías descriptivas (e.g., **Muy Baja**, **Baja**, **Moderada**, etc.) para facilitar su interpretación.
🎯 **Límites de Desviación (Superior e Inferior)**
- Los límites superior e inferior representan un **rango proyectado** en torno al precio futuro estimado, proporcionando un marco para la incertidumbre.
- Estos límites se calculan ajustando el ATR según:
- Un **multiplicador** definido por el usuario (`factor_desviacion`).
- Las **probabilidades condicionales** calculadas previamente.
- La **raíz cuadrada del período proyectado** (`proyeccion_dias`), lo que incorpora el principio de que la incertidumbre aumenta con el tiempo.
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🔍 **Interpretación del Modelo**
Este modelo se puede interpretar como un **modelo probabilístico dinámico** que:
- Integra **análisis técnico** (tendencias y ATR).
- Ajusta probabilidades utilizando **la teoría de Bayes**.
- Proporciona un **rango de proyección visual** para ayudarte a entender los posibles movimientos futuros del precio y su incertidumbre.
⚡ Ya sea que estés analizando **mercados volátiles** o confirmando **escenarios alcistas/bajistas**, ¡esta herramienta te ofrece un enfoque robusto y basado en datos! 🚀
