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 ${\chi }^2$ 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.

Keywords:

• Modified box M test
• homogeneity of several covariance matrices
• non-normal distribution
• dependent stationary process
• high-dimensional data

Additional information

Funding

This work was supported by National Basic Research Program of China (973 Program, 2015CB856004) and the National Natural Science Foundation of China (11531001).