Stationary subspace analysis based on second-order statistics

TL;DR

This paper extends stationary subspace analysis (SSA) to detect nonstationarities in mean, variance, and autocorrelation, improving the identification of stationary and nonstationary components in multivariate time series.

Contribution

It introduces SSA methods capable of detecting multiple types of nonstationarities, enhancing the classical approach that only considers mean and variance.

Findings

Proposed methods outperform classical SSA in various settings.

Detection of all three nonstationarity types improves component separation.

Simulation studies validate the effectiveness of the new SSA techniques.

Abstract

In stationary subspace analysis (SSA) one assumes that the observable p-variate time series is a linear mixture of a k-variate nonstationary time series and a (p-k)-variate stationary time series. The aim is then to estimate the unmixing matrix which transforms the observed multivariate time series onto stationary and nonstationary components. In the classical approach multivariate data are projected onto stationary and nonstationary subspaces by minimizing a Kullback-Leibler divergence between Gaussian distributions, and the method only detects nonstationarities in the first two moments. In this paper we consider SSA in a more general multivariate time series setting and propose SSA methods which are able to detect nonstationarities in mean, variance and autocorrelation, or in all of them. Simulation studies illustrate the performances of proposed methods, and it is shown that especially the method that detects all three types of nonstationarities performs well in various time series settings. The paper is concluded with an illustrative example.