Linear Combination Test for Detecting Serial Correlation in Multivariate Samples

摘要

This document proposes a test for detecting serial dependence among multivariate observations. The test statistic is the maximum absolute value of the lag 1 correlation obtainable from a linear combination of the observations. The authors express the statistic in terms of two eigenvalues and then obtain the asymptotic null distribution. Asymptotic power is examined for sequences of local alternatives in a multivariate normal autoregressive process. An explicit expression is obtained for the density of the limit distribution in the bivariate case. They then compare power with the likelihood ratio statistic. (Author)