Stationary subspace analysis based on second-order statistics

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.

References in corpus (10)

• Fourth Moments and Independent Component Analysis
• Feature Extraction for Change-Point Detection using Stationary Subspace Analysis
• Separation of uncorrelated stationary time series using autocovariance matrices
• Asymptotic and bootstrap tests for subspace dimension
• Asymptotic and bootstrap tests for the dimension of the non-Gaussian subspace
• Extracting conditionally heteroscedastic components using ICA
• Sliced Average Variance Estimation for Multivariate Time Series
• TBSSvis: Visual Analytics for Temporal Blind Source Separation
• Geometry-aware stationary subspace analysis
• Averaging orthogonal projectors

Cited by in corpus (1)

• Identifiable Autoregressive Variational Autoencoders for Nonlinear and Nonstationary Spatio-Temporal Blind Source Separation