V.2:4 (116-122): Fourier Spectral Analysis by William T. Taylor

Fourier Spectral Analysis by William T. Taylor

Introduction

Because many commodity and stock prices appear to exhibit some cyclical movement, it is important for the trader who relies on this characteristic feature to recognize these cycles and adjust the parameters of the particular technical trading system in use, accordingly. For example, the trader may wish to filter out or accentuate cycles of particular lengths using moving averages, Commodity Channel Index, or any number of popular trading systems.

Some cycles can be seen, more or less, on the price charts from commercial charting services or computer-generated charts from some of the popular microcomputer programs available to the trader. I say "more or less" because these charts show only a relatively short time period on each page, particularly if the data is on a daily basis.

Wouldn't it be nice if there were some technique for identifying and categorizing cyclical components by various frequencies and amplitudes, given actual price data over relatively long time periods? Well, there is such a technique. It is called Spectral Analysis.

Derived from the word spectrum, meaning a continuous sequence or range, Spectral Analysis is a statistical procedure used to evaluate a time series of data that produces an evaluation of the various cyclical components of that data. It is based on a mathematical concept called Fourier Analysis, named after the French mathematician Jean Baptiste Joseph Fourier. The fundamental theory of Fourier Analysis is that any time series is made up of components of sine and cosine wave forms of various frequencies and amplitudes. These components are summed for each point in the time series to produce a frequency/amplitude series of data, called a Fourier Series.