Bollinger Bands - Statistical Properties

Statistical Properties

Security price returns have no known statistical distribution, normal or otherwise; they are known to have fat tails, compared to a normal distribution. The sample size typically used, 20, is too small for conclusions derived from statistical techniques like the central limit theorem to be reliable. Such techniques usually require the sample to be independent and identically distributed which is not the case for a time series like security prices. In point of fact, just the opposite is true; it is well recognized by practitioners that such price series are very commonly serially correlated – that is, it is the case that the next price will be closely related to its ancestor 'most of the time'.

For these three principal reasons, it is incorrect to assume that the percentage of the data that will be observed in the future outside the Bollinger Bands range will always be constrained to a certain amount. Instead of finding about 95% of the data inside the bands, as would be the expectation with the default parameters if the data were normally distributed, studies have found that only about 88% of security prices remain within the bands. Practitioners may also use related measures such as the Keltner channels, or the related Stoller average range channels, which base their band widths on different measures of price volatility, such as the difference between daily high and low prices, rather than on standard deviation, which is a statistical measure more appropriate to normal distributions.