Testing for multivariate heteroscedasticity

Abstract

In this paper we propose a testing technique for multivariate heteroscedasticity, which is expressed as a test of linear restrictions in a multivariate regression model. Four test statistics with known asymptotical null distributions are suggested, namely the Wald (W), Lagrange Multiplier (LM), Likelihood Ratio (LR) and the multivariate Rao F-test. The critical values for the statistics are determined by their asymptotic null distributions, but also bootstrapped critical values are used. The size, power and robustness of the tests are examined in a Monte Carlo experiment. Our main findings are that all the tests limit their nominal sizes asymptotically, but some of them have superior small sample properties. These are the F, LM and bootstrapped versions of Wand LR tests.