Testing for multivariate autocorrelation

Abstract

This paper concerns the problem of assessing autocorrelation of multivariate (i.e. system wise) models. It is well known that systemwise diagnostic tests for autocorrelation often suffers from poor small sample properties in the sense that the true size overstates the nominal size gravely. The failure of keeping control of the size usually stems from the fact that the critical values (used to decide the rejection area) originate from the slowly converging asymptotic null distribution. Another drawback of existing tests is that the power may be rather low if the deviation from the null is not symmetrical over the marginal models. In this paper we consider four quite different test techniques for autocorrelation. These are (i) Pillai's trace, (ii) Roy's largest root, (iii) the maximum F-statistic and (iv) the maximum (test. We show how to obtain control of the size ofthe tests, and then examine the true (small sample) size and power properties by means of Monte Carlo simulations.