Sparse-Patterned Wavelet Neural Networks and Their Applications to Stock Market Forecasting

A new approach adopted in this chapter is to apply sparse-patterned wavelet neural networks to simulate emerging stock market price movements. The approach is based on wavelet analysis, which is a relatively new and quite powerful mathematical tool for non-linear financial econometrics. Like conventional Fourier time series analysis, it involves the projection of a time-series onto an orthogonal set of components: in the case of Fourier analysis sine and cosine functions; and in the case of wavelet analysis wavelets. A critical difference is that wavelet analysis exhibits the characteristics of the local behavior of the function, whereas Fourier analysis presents the characteristics of the global behavior of the function. Compared to Fourier analysis, wavelet analysis offers several advantages. Fourier analysis decomposes a given function into sinusoidal waves of different frequencies and amplitudes. This is an effective approach when the given function is stationary. However, when the characteristics at each frequency change over time or there are singularities, Fourier analysis will give us the average of the changing frequencies over the whole function, whereas wavelet analysis can tell us how a given function changes from one time period to the next. It does this by matching a wavelet function, of varying scales and positions, to that function.