Bollinger Bands

Two input parameters chosen independently by the user govern how a given chart summarizes the known historical price data, allowing the user to vary the response of the chart to the magnitude and frequency of price changes, similar to parametric equations in signal processing or control systems.

Writing the same symbols as before, and middleBB for the moving average, or middle Bollinger Band: Using the default parameters of a 20-period look back and plus/minus two standard deviations, bandwidth is equal to four times the 20-period coefficient of variation.

In 2007, Lento et al. published an analysis using a variety of formats (different moving average timescales, and standard deviation ranges) and markets (e.g., Dow Jones and Forex).

[6] Analysis of the trades, spanning a decade from 1995 onwards, found no evidence of consistent performance over the standard "buy and hold" approach.

The authors did, however, find that a simple reversal of the strategy ("contrarian Bollinger Band") produced positive returns in a variety of markets.

A recent study examined the application of Bollinger Band trading strategies combined with the ADX for Equity Market indices with similar results.

[8] In 2012, Butler et al. published an approach to fitting the parameters of Bollinger Bands using particle swarm optimization method.

[10] 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.

For such reasons, it is incorrect to assume that the long-term percentage of the data that will be observed in the future outside the Bollinger Bands range will always be constrained to a certain amount.

[14] Bollinger bands have been applied to a "Method to Identify the Start and End of the Winter Surge in Demand for Pediatric Intensive Care in Real-Time.