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Residual-Based Tests for Normality in Autoregressions: Asymptotic Theory and Simulation Evidence

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  • Kilian, Lutz
  • Demiroglu, Ufuk

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.

Suggested Citation

  • Kilian, Lutz & Demiroglu, Ufuk, 2000. "Residual-Based Tests for Normality in Autoregressions: Asymptotic Theory and Simulation Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(1), pages 40-50, January.
    • Handle: RePEc:bes:jnlbes:v:18:y:2000:i:1:p:40-50
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