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This article presents a homogeneity test for testing the equality of severalhigh-dimensional covariance matrices for stationary processes with ignoring theassumption of normality. We give the asymptotic distribution of the proposedtest. The simulation illustrates that the proposed test has perfectperformance. Moreover, the power of the test can approach any high probabilityuniformly on a set of covariance matrices.

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