Residual-Based Tests for Normality in Autoregressions: Asymptotic Theory and Simulation Evidence
证明Jarque-Bera正态性检验在向量误差修正模型和含单位根或协整的VAR模型中渐近有效，并建议在平稳VAR和VEC模型中使用自助法临界值，小样本下自助法比渐近检验更准确。
Abstract 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. KEY WORDS: Asymptotic theoryBootstrapForecastingUnit root