Testing High-dimensional Nonstationary Time Series

TL;DR

This paper develops new theoretical results for the spectral properties of high-dimensional nonstationary time series, introduces a novel unit root test, and empirically examines the PPP hypothesis in high dimensions.

Contribution

It establishes the joint CLT for eigenvalues of correlation matrices in high-dimensional nonstationary processes and proposes a new high-dimensional unit root testing method.

Findings

The joint CLT for extreme eigenvalues is proven for high-dimensional random walks.

A new high-dimensional unit root test is proposed and validated.

Empirical analysis supports the PPP hypothesis in high-dimensional contexts.

Abstract

In this article, we first establish the joint central limit theorem (CLT) for the extreme eigenvalues of the sample correlation matrix of high-dimensional random walks with cross-sectional dependence. We further investigate the asymptotic spectral properties of the sample correlation matrix of high-dimensional autoregressive processes. To apply our theoretical results, we propose a novel high-dimensional unit root test and develop a forward sequential test to determine the number of unit roots in high-dimensional time series data. Finally, we conduct an empirical study of the purchasing power parity (PPP) hypothesis in high-dimensional settings.