Economic prediction by multichannel Wiener filtering



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The principles of multichannel Wiener filtering have been applied to the problem of economic prediction with emphasis on stock market prices. A brief history of the stock market is presented with an explanation of stock theory and mechanics. Although strictly theoretical studies of the stock market are rather rare, there have been several notable exceptions dating from a study of the Vienna market in 1871. Most early investigators came to the same general conclusion, that stock price changes can best be described as a random walk and are therefore completely unpredictable. More recently, however, several authors using various methods have shown that there are indications of trends in the market which tend to persist. If autocorrelations of the price changes exist for non-zero time shifts, then under certain conditions the series will be susceptible to the principles of Wiener filtering. Given a multichannel input time series the filter is derived under the criterion that it will minimize the mean-squared error between the input series and the predicted series. A simple example is presented to illustrate the computations involved. The three channels used for the stock prediction consist of the stock price data, Dow-Jones Average data, and volume of sales data, respectively. It is shown how these series are modified so as to conform best to the assumption of wide-sense stationarity in the series. A computer program was written to test the predictability of five stocks using one, two, and three input channels. Each predicted value is compared to that which subsequently occurred. An explanation is given for each of the various computer plots and listings obtained in the analysis. The predicted values which were obtained were generally no more accurate than a simple linear trend, which indicates that the price changes are indeed nearly unpredictable. However, suggestions for improvement are given for testing these and other time series.