Multiresolution methods for financial time series prediction

Summary form only given. Fractional Brownian motion (fBm), a 1/f, fractal process, has long been considered a plausible model for financial time series. A fractal structure of the market, indicating the presence of correlations across time, hints at the possibility of some predictability. Recent advances in time/frequency localized transforms by the applied mathematics and electrical engineering communities provide us with powerful new methods for the analysis of this type of process. In fact, it has been proven by Wornell that the wavelet transform is an optimal (KL) transform for fBm processes. With this result, we consider using the wavelet decomposition to analyze financial time series. Specifically, the discrete wavelet transform can be used to decompose a signal into several scales, while maintaining time localization of events in each scale. In terms of financial time series, we can conceptually think of each of these scales as the contribution to the price movement from the information and traders associated with a given investment horizon, for instance, long term traders, such as institutional investors, basing their trades on long term information, form the low-frequency component of the market. Once we have extracted out these scales, we can view each as a stationary time series, which can be modeled, analyzed and predicted individually, either independently, or in conjunction with other scales and data that is relevant to that scale. For the case of prediction, the forecasts from each scale can be fused together, with traditional techniques such as hard coded decision rules, or with a neural network, to arrive at tomorrow´s direction and/or price