Homogeneity test of several high-dimensional covariance matrices for stationary processes under non-normality

Abstract

We propose a test for testing the equality of several high-dimensional covariance matrices for stationary processes with a general distribution. The asymptotic distribution of the proposed test is proved to be distribution. Both the numerical simulation and empirical study illustrate that the proposed test has perfect performance, in particular, its power can approach to 1 on a set of covariance matrices with three known distributions.