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A Distance Test of Normality for a Wide Class of Stationary Processes

Author

Listed:
  • Zacharias Psaradakis

    (Birkbeck, University of London)

  • Marián Vávra

    (National Bank of Slovakia)

Abstract

This paper considers a distance test for normality of the one-dimensional marginal distribution of stationary fractionally integrated processes. The test is implemented by using an autoregressive sieve bootstrap approximation to the null sampling distribution of the test statistic. The bootstrap-based test does not require knowledge of either the dependence parameter of the data or of the appropriate norming factor for the test statistic. The small-sample properties of the test are examined by means of Monte Carlo experiments. An application to real-world data is also presented.

Suggested Citation

  • Zacharias Psaradakis & Marián Vávra, 2015. "A Distance Test of Normality for a Wide Class of Stationary Processes," Birkbeck Working Papers in Economics and Finance 1513, Birkbeck, Department of Economics, Mathematics & Statistics.
  • Handle: RePEc:bbk:bbkefp:1513
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    References listed on IDEAS

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    1. Bontemps, Christian & Meddahi, Nour, 2005. "Testing normality: a GMM approach," Journal of Econometrics, Elsevier, vol. 124(1), pages 149-186, January.
    2. 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.
    3. Lobato, Ignacio N. & Velasco, Carlos, 2004. "A Simple Test Of Normality For Time Series," Econometric Theory, Cambridge University Press, vol. 20(04), pages 671-689, August.
    4. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," Review of Economic Studies, Oxford University Press, vol. 61(4), pages 631-653.
    5. Justel, Ana & Peña, Daniel & Zamar, Rubén, 1997. "A multivariate Kolmogorov-Smirnov test of goodness of fit," Statistics & Probability Letters, Elsevier, vol. 35(3), pages 251-259, October.
    6. D. S. Poskitt, 2008. "Properties of the Sieve Bootstrap for Fractionally Integrated and Non-Invertible Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(2), pages 224-250, March.
    7. Yoosoon Chang & Joon Y. Park, 2003. "A Sieve Bootstrap For The Test Of A Unit Root," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 379-400, July.
    8. Cotter, John, 2007. "Varying the VaR for unconditional and conditional environments," Journal of International Money and Finance, Elsevier, vol. 26(8), pages 1338-1354, December.
    9. D. Poskitt, 2007. "Autoregressive approximation in nonstandard situations: the fractionally integrated and non-invertible cases," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(4), pages 697-725, December.
    10. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    11. Donald W. K. Andrews & Yixiao Sun, 2004. "Adaptive Local Polynomial Whittle Estimation of Long-range Dependence," Econometrica, Econometric Society, vol. 72(2), pages 569-614, March.
    12. Jushan Bai & Serena Ng, 2005. "Tests for Skewness, Kurtosis, and Normality for Time Series Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 49-60, January.
    13. Runde, Ralf, 1997. "The asymptotic null distribution of the Box-Pierce Q-statistic for random variables with infinite variance an application to German stock returns," Journal of Econometrics, Elsevier, vol. 78(2), pages 205-216, June.
    14. Palm, Franz C. & Smeekes, Stephan & Urbain, Jean-Pierre, 2010. "A Sieve Bootstrap Test For Cointegration In A Conditional Error Correction Model," Econometric Theory, Cambridge University Press, vol. 26(03), pages 647-681, June.
    15. Hassler, Uwe & Kokoszka, Piotr, 2010. "Impulse Responses Of Fractionally Integrated Processes With Long Memory," Econometric Theory, Cambridge University Press, vol. 26(06), pages 1855-1861, December.
    16. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
    17. Edwin Choi & Peter Hall, 2000. "Bootstrap confidence regions computed from autoregressions of arbitrary order," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 461-477.
    18. Mohamed Boutahar, 2010. "Behaviour of skewness, kurtosis and normality tests in long memory data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(2), pages 193-215, June.
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    Cited by:

    1. Zacharias Psaradakis & Marian Vavra, 2017. "Normality Tests for Dependent Data," Working and Discussion Papers WP 12/2017, Research Department, National Bank of Slovakia.
    2. Marian Vavra, 2018. "Assessing Distributional Properties of Forecast Errors," Working and Discussion Papers WP 3/2018, Research Department, National Bank of Slovakia.

    More about this item

    Keywords

    Distance test; fractionally integrated process; Sieve bootstrap; normality.;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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