Mark Temple-Raston, PhD., Precision Alpha
Bollinger bands are seen to capture fundamental market behavior, and are often used to identify trading opportunities. In the early 2000’s, our original motivation for Precision Alpha was to recast Bollinger bands and MACD so as to clarify scientifically the origin and meaning of the observed market behavior.
Unfortunately, however, Bollinger bands have several arbitrary parameters to play with, specifically, the duration of the moving window used to calculate the mean, and the number of standard deviations from the mean. Since standard deviation is a statistical equilibrium concept derived from the more general (non-equilibrium) variance, and markets are clearly not in statistical equilibrium, it was clear that Bollinger bands would need to be stripped of their standard deviations to achieve a scientific understanding of the non-equilibrium market behavior.
Similarly, MACD (Mean Average Convergence/Divergence) introduces two different user-specified and arbitrary time-scales (a long, and a short) for moving windows. MACD is used to identify when the long and short time-scale means converge or diverge. A trading time-horizon could set the short time-scale, but not both long and short (two variables, one constant).
Precision Alpha calculates the daily, non-equilibrium probabilities exactly through scientific learning. The arbitrary standard deviations are replaced with the maximum and minimum probabilities (turning points for the exact probabilities). This eliminates entirely the parameter associated with the number of standards deviations.
Moreover, when an infinite number of market days is used (if that were physically possible), then mathematically (from the central limit theorem) the market behavior would converge to statistical equilibrium (that is, the price is just as likely to go up as to go down). By selecting a short time-scale appropriate to the trading horizon and the long time-scale to be infinite, MACD is now recast to be the convergence to or divergence from statistical equilibrium. Since statistical equilibrium is well-defined (probability is 50-50), an infinite amount of data is not required to calculate the MACD.
By plotting the learned probabilities produced by Precision Alpha, the Bollinger Bands and MACD are replaced with specific scientific quantities, with no arbitrary, user-supplied parameters required.
An even greater understanding of financial market dynamics is achieved by calculating additional market features, for example, market energy, market power, market resistance and market noise/efficiency.
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