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Confidence Region for long memory based on Inverting Bootstrap Tests: an application to Stock Market Indices

Author

Listed:
  • Christian De Peretti

    (Centre d’Etudes des Politiques Economiques (EPEE), University of Evry Val d’Essonne)

  • Carole Siani

    (Laboratoire d’InfoRmatique en Image et Syst`emes d’Information (LIRIS), University of Claude Bernard Lyon 1)

Abstract

In the context of long memory, the finite-sample distortion of statistic distributions is so large, that bootstrap confidence intervals (percentile and percentile-t) for the long memory parameter do not perform better than the corresponding asymptotic confidence interval. In this paper, we propose confidence intervals based on inverting bootstrap tests for the long memory parameter in the ARFIMA model. We show that classical confidence intervals have very poor performances, even the percentile-t interval, whereas confidence intervals based on inverting bootstrap tests have quite satisfactory performance. For this purpose, we use techniques for measuring effectiveness of confidence regions and for the graphical display of simulation evidence concerning the coverage and effectiveness of confidence regions in finite sample. Monte Carlo results on the confidence intervals for various situations are presented. These intervals are then applied on stock market indices.

Suggested Citation

  • Christian De Peretti & Carole Siani, 2008. "Confidence Region for long memory based on Inverting Bootstrap Tests: an application to Stock Market Indices," Documents de recherche 08-02, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
  • Handle: RePEc:eve:wpaper:08-02
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    File URL: http://epee.univ-evry.fr/RePEc/2008/08-02.pdf
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    Keywords

    Long memory; confidence interval; inverting tests; bootstrap; graphical method;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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