This script calculates upper and lower bands using Chebyshev's inequality formula.
The main pros.: the band doesn't depend on particular distribution. It fits to any type of random variables. Also it allows to calculate bands for instruments with extremely high volatility.
Cons.: formula provides a rough estimation in some special cases like lognormal distribution.
@sthlm08, Chebyshevs Bands (CBs) are similar to Bollinger Bands (BBs), but there are some differences: 1. CBs are calculated relative to a previous close price while BBs use last MA value. It makes sense if we assume that daily price changes are a random variable. 2. CBs transform price changes to exponential form. It guarantees that the price value will be positive. Hypothetically the low band of BBs could be negative on high volatile instruments. 3. CBs allow to remove a trending component: average shift. It makes sense if we assume that an actual average price change is zero.
konstantin.novik
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@Konstantin.novik, of course, it could be applied to any timeframe. In that case we assume that the changes on the timeframe is random.
Sonoluminescence
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@Konstantin.novik, Thank you Konstantin for the explanation. However if you would be able to clarify with a image of an example on what to look for within the bands it would be really helpful. Since the candles never crosses the bands nor dose it have a baseline it makes me confused on what type of pattern to look out for. Thanks again for your work.
Sonoluminescence
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@sthlm08, Sorry I see now that candles sometime does cross the lines but most often in periods with extreme movements. Still would like to know what to make out of it.
I think that the crossing of the channel shows the key point to think and analyse the situation. If we believe that the movement is random, the next move should not depend from the previous. So, rebound from the channel is ... an odd scenario. But maybe it makes sense to estimate the situation.
If we don't believe the random nature of prices than channels with probabilistic parameters have no sense at all :)
Of course, I oversimplified the argumentation.
Sonoluminescence
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@Konstantin.novik, Thank you it makes much more sense now :) I like the idea very much and will study it more. I think it could be very useful.