Testing for parameter restrictions in a stationary VAR model: A bootstrap alternative

Abstract

This paper proposes the use of the bootstrap when the system Wald test is employed to test for linear restrictions in a stationary vector autoregressive (VAR) model. The bootstrap test is conducted using the estimated generalised least square estimator for VAR parameters, which considers contemporaneous correlations among the error terms. It is found that the bootstrap test shows little size distortion in small samples. In contrast, the asymptotic Wald test exhibits serious size distortion, severely over-rejecting the true null hypothesis in small samples. The bootstrap test also has desirable power properties, with its power particularly high when the model is near non-stationary and the error terms are highly correlated contemporaneously. As an application, the bootstrap Wald test is employed to test for the predictability of stock return from dividend yield using U.S. data.