Quantitative Analysis  |  JAN 2007

Fourier Transform For Traders by John F. Ehlers

Stocks & Commodities V. 25:1 (24-34): Fourier Transform For Traders by John F. Ehlers When market conditions are variable, adapting to them becomes a challenge. Here’s how you can use a dominant cycle to tune the relevant indicators so you don’t have to drive through the fog. It is intrinsically wrong to use a 14-bar relative strength index (RSI), a nine-bar stochastic, a 5/25 double moving average crossover, or any other fixed-length indicator when the market conditions are variable. It’s like driving on a curving mountain road in a fog bank with your cruise control locked — and you’ve desperately got to clean your eyeglasses. That market conditions are continuously changing is not even a subject of debate. There have been a number of attempts to adapt to changing market conditions. Volatility-based nonlinear moving averages are just one example of adapting to market changes. As I come from an information theory background, my answer to the question of how to adapt to changing conditions is to first measure the dominant market cycle and then tune the various indicators to that cycle period, or at least a fraction of it. Theoretically, an RSI performs best when the computation period is just half of a cycle period — that is, when all the movement is in one direction and then reverses so all the movement is in the other direction over the period of one cycle — and you get a full amplitude swing from the RSI.

by John F. Ehlers