Measuring predictability using multiresolution 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 the lower frequencies are 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 solution to this problem. Using multiresolution analysis we separate the different time-scales in a given time series. By separating the time series into its component time-scales using the translation-invariant wavelet transform, we will determine at which time-scale the series is most predictable.