Moving Window—Spectral Method: Price
Forecasting With Cycles
by A.D. Ridley, Ph.D.
I would-like to introduce a new method of stock market forecasting with a practical application. The
Moving Window-Spectral (MWS) method  takes advantage of the cyclical nature of stock, bond,
commodity and other prices to forecast prices. I've included an example to illustrate systematic
estimation and forecasting, and a trading rule as well.
While the theory on which the following discussion is based is applicable to multivariate time series
analysis, trading an index, stock or commodity, is a univariate application. In univariate time series
analysis, only a single variable is examined. One price time series is all that is required for the
examination . I believe multivariate analysis is not likely to add very much to stock market analysis and
forecasting. (Even if other explanatory variables were helpful, they would not be known to the trader. In
order to be useful input, other variables must be known in advance. This is rarely possible.)
Univariate analysis does not implicitly deny the existence and relevance of other variables. Instead it is
assumed that their effects are embedded in the time series. The emphasis then, must be on efficient
methods of extracting this imbedded information from the time series.
The Moving Window-Spectral (MWS) is a computer algorithm that takes advantage of the cyclical nature
of the stock market to perform information extraction. The computer code performs two stages of
execution. In the first stage, a history of observations is examined, and the relationship between values in
different time periods calculated.
The relationships are represented as numerical parameters. In the second stage, these parameters are used
to estimate future values from the time series. These estimates comprise the forecast on which the trader
may base decision-making.