|  NOV 1987

How to use Maximum Entropy by John F. Ehlers

How to use Maximum Entropy by John F. Ehlers MESA is an acronym for Maximum Entropy Spectrum Analysis, a forecasting method that filters the ""noise"" from time series data and can uncover useful cycles. The advantages of the maximum entropy method over Fourier analysis is that high-resolution identification of cycles is possible using an extremely short database. This is important for short-term trading because cycles can fade or change before they are recognized by more conventional approaches. Maximum entropy also is not subject to the windowing or end-effect distortions that Fourier transforms suffer because it extracts nearly all the coherent cycle ""energy"" in a set of data. The noise or useless information (""entropy"") that clutters up data and hides cycles is filtered out like so much chaff. Cycles are related to random walk The reason the short-term cycles appear, fade and alter is that they arise as solutions to a class of random walk problems. Though it may seem so, random walk does not necessarily mean chaos. Mathematicians call the problem class in which we are interested the ""drunkard's walk."" The problem is formulated by allowing the drunkard to step either to the right or to the left as he steps forward. To ensure randomness, the drunkard must flip a fair coin to determine the direction of his next step. The differential equation that results from this formulation is called the diffusion equation (Figure 1). The diffusion equation is useful for describing physical phenomena like the plume of smoke leaving a smokestack.

by John F. Ehlers