Homogeneity Test of Several High-Dimensional Covariance Matrices for Stationary Processes under Non-normality

TL;DR

This paper introduces a new homogeneity test for multiple high-dimensional covariance matrices of stationary processes that does not assume normality, with proven asymptotic distribution and strong performance in simulations.

Contribution

It proposes a novel non-normality-assuming homogeneity test for high-dimensional covariance matrices with proven asymptotic properties.

Findings

Test has asymptotic distribution derived.

Simulation shows perfect performance.

Power approaches high probability uniformly.

Abstract

This article presents a homogeneity test for testing the equality of several high-dimensional covariance matrices for stationary processes with ignoring the assumption of normality. We give the asymptotic distribution of the proposed test. The simulation illustrates that the proposed test has perfect performance. Moreover, the power of the test can approach any high probability uniformly on a set of covariance matrices.