Residual-based tests for normality in autoregressions: Asymptotic theory and simulation evidence

Existing results for the asymptotic validity of the Jarque-Bera test in vector autoregressive (VAR) models assume stationarity. In applied work however, researchers often work with possibly integrated and cointegrated process. We prove the asymptotic validity of the Jarque-Bera test for vector error-correction (VEC) models and for unrestricted VAR models with possibly integrated or cointegrated variables. We also propose the use of bootstrap critical values in stationary VAR models and in VEC models. We show that the bootstrap version of the Jarque-Bera test is considerably more accurate in small samples than the asymptotic test, even for processes with roots close to unity.