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Residual-Based Bootstrap Tests for Normality in Autoregressions

Author

Listed:
  • Kilian, L.
  • Demiroglu, U.

Abstract

- It is well known that the asymptotic distribution of residual-based test statistics for normality may provide a poor approximation in finite samples. We propose the use of bootstrap critical values to improve small-sample performance and compare the accuracy of the asymptotic and bootstrap versions of the Bera-Jarque test for normality in autoregressions. The proposed bootstrap test is shown to be considerably more accurate than the asymptotic test for a wide range of univariate and multivariate finite order AR models. It effectively eliminates size distortions. The bootstrap test also has high power against a variety of non-Gaussian alternatives including GARCH innovations. Our results are useful in many areas of forecasting and econometric inference, including maximum likelihood estimation and inference for cointegrated systems, the construction of forecast intervals and multivariate forecast regions for autoregressions, backcasting techniques in conditional bootstrap prediction, tests for structural instability in autoregressions, and resampling techniques based on second-moment approximations.

Suggested Citation

  • Kilian, L. & Demiroglu, U., 1997. "Residual-Based Bootstrap Tests for Normality in Autoregressions," Papers 97-14, Michigan - Center for Research on Economic & Social Theory.
    • Handle: RePEc:fth:michet:97-14
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    Citations

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    Cited by:

    1. DUFOUR, Jean-Marie & JOUINI, Tarek, 2005. "Finite-Sample Simulation-Based Inference in VAR Models with Applications to Order Selection and Causality Testing," Cahiers de recherche 16-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    2. Dufour, Jean-Marie & Jouini, Tarek, 2006. "Finite-sample simulation-based inference in VAR models with application to Granger causality testing," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 229-254.
    3. Bontemps, Christian & Meddahi, Nour, 2005. "Testing normality: a GMM approach," Journal of Econometrics, Elsevier, vol. 124(1), pages 149-186, January.
    4. Kim, Jae H., 2004. "Bootstrap prediction intervals for autoregression using asymptotically mean-unbiased estimators," International Journal of Forecasting, Elsevier, vol. 20(1), pages 85-97.

    More about this item

    Keywords

    FORECASTING ; TESTS ; ECONOMIC MODELS;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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