V.12:3 (121-124): Optimal Window Length For Forecasting by A. Denis Ridley, Ph.D.

V.12:3 (121-124): Optimal Window Length For Forecasting by A. Denis Ridley, Ph.D.
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Optimal Window Length For Forecasting by A. Denis Ridley, Ph.D.

As a rule, the financial markets are complex and difficult to analyze, due to multiple cyclical elements present in the related data. The moving window spectral (Mws) method of analysis and forecasting decomposes the data into a spectrum of cyclical components; this is important because each cyclical component can be evolving over time, in its own unique way. Both the magnitude and phase of each cycle may change independently. To determine how each component is changing, a window with a fixed length of time is moved along the data. At each data point, each cycle is examined and recorded as an observation. From this data, the way in which each cycle evolves may be calculated. Then each component is forecast separately. The component forecasts are then integrated to determine the final forecast.

To accomplish all this, what is the best window length? To determine the optimum, we will use the Dow Jones Industrial Average (DJIA). The same principles can also be applied to other stock market prices and price indices.

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