A test for constant correlations in a multivariate GARCH model

We introduce a Lagrange Multiplier (LM) test for the constant-correlation hypothesis in a multivariate GARCH model. The test examines the restrictions imposed on a model which encompasses the constant-correlation multivariate GARCH model. It requires the estimates of the constant-correlation model only and is computationally convenient. We report some Monte Carlo results on the finite-sample properties of the LM statistic. The LM test is compared against the Information Matrix (IM) test due to Bera and Kim (1996). The LM test appears to have good power against the alternatives considered and is more robust to nonnormality. We apply the test to three data sets, namely, spot-futures prices, foreign exchange rates and stock market returns. The results show that the spot-futures and foreign exchange data have constant correlations, while the correlations across national stock market returns are time varying.