A New Test for Checking the Equality of the Correlation Structures of two time Series

An order selection test is proposed to check the equality of two independent stationary time series in their correlation structures. The asymptotic distribution of the order selection test statistic under the null hypothesis is obtained. Furthermore, it is shown that the proposed test is consistent not only under any fixed alternative hypothesis but also under a sequence of local alternative hypotheses. A simulation study is conducted to examine the finite sample performance of the test in comparison to some existing methods. The proposed test is also applied to an analysis of a biomedical data set.