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February 2021 Stationary subspace analysis of nonstationary covariance processes: Eigenstructure description and testing
Raanju R. Sundararajan, Vladas Pipiras, Mohsen Pourahmadi
Bernoulli 27(1): 381-418 (February 2021). DOI: 10.3150/20-BEJ1243

Abstract

Stationary subspace analysis (SSA) searches for linear combinations of the components of nonstationary vector time series that are stationary. These linear combinations and their number define an associated stationary subspace and its dimension. SSA is studied here for zero mean nonstationary covariance processes. We characterize stationary subspaces and their dimensions in terms of eigenvalues and eigenvectors of certain symmetric matrices. This characterization is then used to derive formal statistical tests for estimating dimensions of stationary subspaces. Eigenstructure-based techniques are also proposed to estimate stationary subspaces, without relying on previously used computationally intensive optimization-based methods. Finally, the introduced methodologies are examined on simulated and real data.

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Raanju R. Sundararajan. Vladas Pipiras. Mohsen Pourahmadi. "Stationary subspace analysis of nonstationary covariance processes: Eigenstructure description and testing." Bernoulli 27 (1) 381 - 418, February 2021. https://doi.org/10.3150/20-BEJ1243

Information

Received: 1 April 2019; Revised: 1 May 2020; Published: February 2021
First available in Project Euclid: 20 November 2020

zbMATH: 07282855
MathSciNet: MR4177374
Digital Object Identifier: 10.3150/20-BEJ1243

Keywords: dimension test , eigen-decomposition , local and global dimensions , multivariate nonstationarity

Rights: Copyright © 2021 Bernoulli Society for Mathematical Statistics and Probability

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Vol.27 • No. 1 • February 2021
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