Measuring predictability using multiscale embedding

The standard method of embedding time series data is to use a moving window of past values. By the inverse relationship between time and frequency localization, all information contained in frequencies with a period of more than twice the window size is lost using this scheme. Increasing the window size comes at the price of adding more degrees of freedom, and thereby worsening the curse of dimensionality. Wavelets provide a potential solution to this problem. Using multiresolution analysis we can separate the different time-scales in a given time series. Using the single scale representation of a signal we determine whether this method of embedding will aid in the building of predictive linear models. By separating the time series into its component time-scales, we hope to determine at which time-scale the series is most predictable.