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Wavelets in Forecasting

Wavelet analysis is not a forecasting technique but may help improve our forecasting abilities. Multiresolution analysis decomposes observed series to produce different levels of detail. For sufficiently lengthy time series, a level of decomposition that transforms the observed series into a smoothed representation and low scale details is selected with just enough observations to model then forecast each. An inverse transformation process converts models' fitted values back for comparison with the originally observed sequence. In this paper, monthly sunspot numbers are first transformed using the Haar wavelet providing input data to train using artificial neural networks and genetic programming. Inverse transformation compute fitted and forecasted values of the monthly series. Each technique was used to produce three-year-ahead forecasts for a relatively large number of years into the future. These results should therefore invite more research to improve on the proposed method.