Wavelet methods in (financial) time-series processing

We briefly describe the major advantages of using the wavelet transform for the processing of financial time series on the example of the S&P index. In particular, we show how to uncover the local scaling (correlation) characteristics of the S&P index with the wavelet based effective Hölder exponent (Struzik, in: Fractals: Theory and Applications in Engineering, Dekking, Lévy Véhel, Lutton, Tricot, Springer, Berlin, 1999; Fractals 8 (2) (2000) 163). We use it to display the local spectral (multifractal) contents of the S&P index. In addition to this, we analyse the collective properties of the local correlation exponent as perceived by the trader, exercising various time horizon analyses of the index. We observe an intriguing interplay between such (different) time horizons. Heavy oscillations at shorter time horizons, which seem to be accompanied by a steady decrease of correlation level for longer time horizons, seem to be characteristic patterns before the biggest crashes of the index. We find that this way of local presentation of scaling properties may be of economic importance.