Finance - superimposed cycles

S&P 500 closing prices

Forecasting of financial time-series may be enhanced if we can get at the underlying cycles and fluctuations. Let's see what a wavelet transform can provide.

Wavelet transform

But... "future" information has been used here to provide the wavelet coefficients at each scale. This isn't right!! The following gives a result which respects time. It is an additive decomposition. It is not a wavelet transform (the different scales are not of mean zero). It is based on a sliding, and growing, window, on the basis of which a wavelet transform is carried out.

Time-based multiscale transform

Based on the latter, the first reference cited below finds up to 86% correct prediction of the trend - up or down - 5 days ahead.

To probe further

"Wavelet-Based Feature Extraction and Decomposition Strategies for Financial Forecasting", A Aussem, J Campbell and F Murtagh, Journal of Computational Intelligence in Finance, 1998.

Image and Data Analysis: The Multiscale Approach, J-L Starck, F Murtagh and A Bijaoui, Cambridge University Press, 1998.