Testing High-dimensional Nonstationary Time Series

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.