Complexity Pursuit: Separating Interesting Components from Time Series

A generalization of projection pursuit for time series, that is, signals with time structure, is introduced. The goal is to find projections of time series that have interesting structure, defined using criteria related to Kolmogoroff complexity or coding length. Interesting signals are those that can be coded with a short code length. We derive a simple approximation of coding length that takes into account both the nongaussianity and the autocorrelations of the time series. Also, we derive a simple algorithm for its approximative optimization. The resulting method is closely related to blind separation of nongaussian, time-dependent source signals.