Exact tests for serial correlation in vector processes

ABSTRACT Exact tests for serial independence in vector Markoff processes have been obtained by considering the system of regressions of the vectors observed at time 2 t on the vectors observed at times (2 t − 1) and (2 t + 1). The tests then reduce to those obtained from canonical correlation procedures in multivariate analysis. Two particular cases are (1) The test for serial independence of a vector of residuals from a system of regressions in which the regressors are all independent of the residuals. At the same time a test of the hypothesis that the regressor and regrediend vectors are independent is obtained. (2) The test for serial correlation or partial serial correlation in a multiple Markoff process (autoregressive process). An investigation of the efficiency of the test so obtained, of the hypothesis that a process is a simple Markoff process (against the alternative that the process is a second-order auto-regression) suggests that the efficiency of all of these tests will be low.