Principal component analysis in the wavelet domain

Abstract

This paper proposes a new principal component analysis method in the wavelet domain, which is useful for dimension reduction and feature extraction of multiple non-stationary time series. The proposed method is constructed using a novel combination of eigenanalysis and the local wavelet spectrum defined in the locally stationary wavelet process. Therefore, we can expect the proposed method to reflect a more generalized non-stationary time series beyond some limited types of signals that existing methods have performed. We investigate the theoretical results of estimated principal components and their loadings. The results of numerical examples, including the analysis of real seismic data and financial data, show the promising empirical properties of the proposed approach.