A new method for forecasting stock prices using artificial neural network and wavelet theory

Recently, a new decomposition method known as wavelet decomposition was introduced, which is accomplished through the use of an orthogonal basis consisting of so-called "wavelets". Wavelet analysis is a significant advance over Fourier analysis for two reasons. First, while Fourier analysis gives us only frequency information, wavelet analysis gives us both frequency information and time information. Secondly, wavelet analysis can represent a nonstationary process better than Fourier analysis by allowing us to look at the series through wavelets of variable sizes. While the wavelet theory has brought about significant advancements in representation of functions, not much work on its applicability to forecasting has been made. Although an initial attempt to provide the statistical framework for wavelet analysis was made by (Basseville, et al. 1992a, b), the applicability of wavelet analysis to forecasting needs to be further developed. The purpose of this paper is to introduce new methodologies based on wavelet decomposition that can forecast with greater accuracy than existing models. (1) Several models (including ARIMA, detrending and AR, random walk, and artificial neural network) are applied to the original series (Standard & Poor's 500 Index), and to the wavelet decomposed series. The results from the two approaches are compared to see whether the use of the decomposed series (which is the special smoothed version of the original series) in forecasting yields better results than applying the models directly to the original series. (2) An artificial neural network is incorporated with wavelets to forecast the Standard & Poor's 500 Index. (3) Information on the generating process (i.e. relationship from the decomposed series to the original series) is used for forecasting. The models in (1) which use decomposed series, result in smaller forecasting errors, i.e. RMSPE, MAPE, and TIC, than models where the original series are directly applied. The models described in (3) yield better results than the models described in (1) and (2). Wavelet theory is a concept that will need to be developed further for use in economics and finance. While this paper utilizes the simplest wavelets and a univariate case, it should be possible to employ more complicated wavelets and multivariate cases to see if their use can further advance the role of wavelet theory in forecasting.