Reconstruction of Time Series using Optimal Ordering of ICA Components

Abstract

We investigate the application of Independent Component Analysis (ICA) and the process of optimal ordering of independent components in reconstructing time series generated by mixed independent sources. We use a modified fast neural learning ICA algorithm with a non-linearity dependent on the statistical properties of the observed time series to obtain independent components (IC’s). Experimental results are presented on the reconstruction of both artificial time series and actual time series of currency exchange rates using different error measures. The area of the error profile is introduced as a minimizing parameter to obtain optimal ordered lists of IC’s for the different series. We compare different error measures and different algorithms for determining optimal ordering lists. Our results support the use of an Euclidean error measure for evaluating reconstruction errors and are in favor of a method for obtaining optimal ordering lists based on minimizing the error profile between contributions of independent components in the lists and the observed time series. For the majority of the series considered, we find that quite acceptable reconstructions can be obtained with only the first few dominant IC’s in the lists.