Moment Preserving Approximation of Independent Components for the Reconstruction of Multivariate Time Series

Abstract

The application of Independent Component Analysis (ICA) has found considerable success in problems where sets of observed time series may be considered as results of linearly mixed instantaneous source signals. The Independent Components (IC’s) or features can be used in the reconstruction of observed multivariate time seriesfollowing an optimal ordering process. For trend discovery and forecasting, the generated IC’s can be approximated for the purpose of noise removal and for the lossy compression of the signals.We propose a moment-preserving (MP) methodology for approximating IC’s for the reconstruction of multivariate time series.The methodologyis based on deriving the approximation in the signal domain while preserving a finite number of geometric moments in its Fourier domain.Experimental results are presented onthe approximation of both artificial time series and actual time series of currency exchange rates. Our results show that the moment-preserving (MP) approximations of time series are superior to other usual interpolation approximation methods, particularly when the signals contain significant noise components. The results also indicate that the present MP approximations have significantly higher reconstruction accuracy and can be used successfully for signal denoising while achieving in the same time high packing ratios. Moreover, we find that quite acceptable reconstructions of observed multivariate time series can be obtained with only the first few MP approximated IC’s.