Complexity pursuit for unifying time series

Complexity pursuit is a recently developed algorithm using the gradient descent for separating interesting components from time series. It is an extension of projection pursuit to time series data and the method is closely related to blind separation of time-dependent source signals and independent component analysis. The goal is to find projections of time series that have interesting structure, defined using criteria related to Kolmogoroff complexity or coding length. In this paper, we derived a simple approximation of coding length that takes into account the nongaussianity, the autocorrelations and the variance nonstationary of the time series. We give a simple algorithm for its approximative optimization.