Scale space multiresolution correlation analysis for time series data

We propose a new scale space method for the discovery of structure in the correlation between two time series. The method considers the possibility that correlation may not be constant in time and that it might have different features when viewed at different time scales. The time series are first decomposed into additive components corresponding to their features in different time scales. Temporal changes in correlation between pairs of such components are then explored by using weighted correlation within a sliding time window of varying length. Bayesian, sampling-based inference is used to establish the credibility of the correlation structures thus found and the results of analyses are summarized in scale space feature maps. The performance of the method is demonstrated using one artificial and two real data sets. The results underline the usefulness of the scale space approach when the correlation between the time series exhibit time-varying structure in different scales.