Testing for serial correlation in multivariate regression models

This paper considers the problem of detecting serial correlation in the disturbances of a multivariate regression model, when these are known to be correlated up to a known finite lag Q ≥ 0 and are possibly conditionally heteroskedastic. We extend the results of Cumby and Huizinga (1992) to the case of a linear dynamic system of equations, and derive the asymptotic distribution of a vector of sample autocovariances of the regression residuals. This distribution is used to construct a test for serial correlation at lags greater than Q. A comparative Monte Carlo study of the small-sample behavior of various tests in the case of purely autoregressive series reveals that the proposed test performs satisfactorily, while tests that are commonly used in the literature are found to lead to serious size distortions under conditional heteroskedasticity.