IDEAS home Printed from https://ideas.repec.org/p/bbk/bbkefp/1513.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: https://eprints.bbk.ac.uk/id/eprint/15266
    File Function: First version, 2015
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. Malin Adolfson & Jesper Linde & Mattias Villani, 2007. "Forecasting Performance of an Open Economy DSGE Model," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 289-328.
    4. Zacharias Psaradakis, 2016. "Using the Bootstrap to Test for Symmetry Under Unknown Dependence," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 406-415, July.
    5. Lobato, Ignacio N. & Velasco, Carlos, 2004. "A Simple Test Of Normality For Time Series," Econometric Theory, Cambridge University Press, vol. 20(4), pages 671-689, August.
    6. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(4), pages 631-653.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    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. 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.
    14. Jansen, Dennis W & de Vries, Casper G, 1991. "On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 18-24, February.
    15. Hassler, Uwe & Kokoszka, Piotr, 2010. "Impulse Responses Of Fractionally Integrated Processes With Long Memory," Econometric Theory, Cambridge University Press, vol. 26(6), pages 1855-1861, December.
    16. Melvin J. Hinich, 1982. "Testing For Gaussianity And Linearity Of A Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 3(3), pages 169-176, May.
    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.
    19. 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(3), pages 647-681, June.
      • Arnold Zellner & Franz C. Palm, 2000. "Correction," Econometrica, Econometric Society, vol. 68(5), pages 1293-1294, September.
    20. George Kapetanios & Zacharias Psaradakis, 2006. "Sieve Bootstrap for Strongly Dependent Stationary Processes," Working Papers 552, Queen Mary University of London, School of Economics and Finance.
    21. Silvia Goncalves & Lutz Kilian, 2007. "Asymptotic and Bootstrap Inference for AR(∞) Processes with Conditional Heteroskedasticity," Econometric Reviews, Taylor & Francis Journals, vol. 26(6), pages 609-641.
    22. 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.
    23. 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.
    24. 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.
    25. George Kapetanios & Zacharias Psaradakis, 2006. "Sieve Bootstrap for Strongly Dependent Stationary Processes," Working Papers 552, Queen Mary University of London, School of Economics and Finance.
    26. Paparoditis, Efstathios, 1996. "Bootstrapping Autoregressive and Moving Average Parameter Estimates of Infinite Order Vector Autoregressive Processes," Journal of Multivariate Analysis, Elsevier, vol. 57(2), pages 277-296, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Marián Vávra, 2020. "Assessing distributional properties of forecast errors for fan-chart modelling," Empirical Economics, Springer, vol. 59(6), pages 2841-2858, December.
    2. Zacharias Psaradakis & Marian Vavra, 2017. "Normality Tests for Dependent Data," Working and Discussion Papers WP 12/2017, Research Department, National Bank of Slovakia.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zacharias Psaradakis & Marián Vávra, 2017. "Normality Tests for Dependent Data: Large-Sample and Bootstrap Approaches," Birkbeck Working Papers in Economics and Finance 1706, Birkbeck, Department of Economics, Mathematics & Statistics.
    2. Marian Vavra, 2015. "On a Bootstrap Test for Forecast Evaluations," Working and Discussion Papers WP 5/2015, Research Department, National Bank of Slovakia.
    3. Marián Vávra, 2020. "Assessing distributional properties of forecast errors for fan-chart modelling," Empirical Economics, Springer, vol. 59(6), pages 2841-2858, December.
    4. Margherita Gerolimetto & Stefano Magrini, 2020. "Testing for boundary conditions in case of fractionally integrated processes," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(2), pages 357-371, June.
    5. Bontemps, Christian & Meddahi, Nour, 2005. "Testing normality: a GMM approach," Journal of Econometrics, Elsevier, vol. 124(1), pages 149-186, January.
    6. Kontogeorgos, Georgios & Lambrias, Kyriacos, 2019. "An analysis of the Eurosystem/ECB projections," Working Paper Series 2291, European Central Bank.
    7. Zacharias Psaradakis & Marian Vavra, 2018. "Bootstrap Assisted Tests of Symmetry for Dependent Data," Working and Discussion Papers WP 5/2018, Research Department, National Bank of Slovakia.
    8. Poskitt, D.S. & Grose, Simone D. & Martin, Gael M., 2015. "Higher-order improvements of the sieve bootstrap for fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 188(1), pages 94-110.
    9. D.S. Poskitt & Gael M. Martin & Simone D. Grose, 2012. "Bias Reduction of Long Memory Parameter Estimators via the Pre-filtered Sieve Bootstrap," Monash Econometrics and Business Statistics Working Papers 8/12, Monash University, Department of Econometrics and Business Statistics.
    10. Wolfgang Härdle & Joel Horowitz & Jens‐Peter Kreiss, 2003. "Bootstrap Methods for Time Series," International Statistical Review, International Statistical Institute, vol. 71(2), pages 435-459, August.
    11. Zacharias Psaradakis & Marián Vávra, 2015. "A Quantile-based Test for Symmetry of Weakly Dependent Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(4), pages 587-598, July.
    12. Matei Demetrescu & Robinson Kruse-Becher, 2021. "Is U.S. real output growth really non-normal? Testing distributional assumptions in time-varying location-scale models," CREATES Research Papers 2021-07, Department of Economics and Business Economics, Aarhus University.
    13. Yong Bao, 2013. "On Sample Skewness and Kurtosis," Econometric Reviews, Taylor & Francis Journals, vol. 32(4), pages 415-448, December.
    14. Demetrescu, Matei & Kruse, Robinson, 2015. "Testing heteroskedastic time series for normality," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113221, Verein für Socialpolitik / German Economic Association.
    15. G. Kontogeorgos & K. Lambrias, 2022. "Evaluating the Eurosystem/ECB staff macroeconomic projections: The first 20 years," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(2), pages 213-229, March.
    16. Chen, Yi-Ting, 2012. "A simple approach to standardized-residuals-based higher-moment tests," Journal of Empirical Finance, Elsevier, vol. 19(4), pages 427-453.
    17. Berkowitz, J. & Birgean, I. & Kilian, L., 1999. "On the Finite-Sample Accuracy of Nonparametric Resampling Algorithms for Economic Time Series," Papers 99-01, Michigan - Center for Research on Economic & Social Theory.
    18. Jeremy Berkowitz & Lutz Kilian, 2000. "Recent developments in bootstrapping time series," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 1-48.
    19. F. Javier Mencía & Enrique Sentana, 2004. "Estimation and Testing of Dynamic Models with Generalised Hyperbolic Innovations," Working Papers wp2004_0411, CEMFI.
    20. Härdle, Wolfgang & Horowitz, Joel L. & Kreiss, Jens-Peter, 2001. "Bootstrap methods for time series," SFB 373 Discussion Papers 2001,59, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.

    More about this item

    Keywords

    Distance test; fractionally integrated process; Sieve bootstrap; normality.;
    All these keywords.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bbk:bbkefp:1513. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://www.bbk.ac.uk/departments/ems/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.