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Nonparametric Beta kernel estimator for long memory time series

Author

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  • BOUEZMARNI, Taoufik

    (University of Sherbrooke, Canada)

  • VAN BELLEGEM, Sébastien

    (Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium; Toulouse School of Economics, France)

Abstract

The paper introduces a new nonparametric estimator of the spectral density that is given in smoothing the periodogram by the probability density of Beta random variable (Beta kernel). The estimator is proved to be bounded for short memory data, and diverges at the origin for long memory data. The convergence in probability of the relative error and Monte Carlo simulations suggest that the estimator automaticaly adapts to the long- or the short-range dependency of the process. A cross-validation procedure is also studied in order to select the nuisance parameter of the estimator. Illustrations on historical as well as most recent returns and absolute returns of the S&P500 index show the reasonable performance of the estimation, and show that the data-driven estimator is a valuable tool for the detection of long-memory as well as hidden periodicities in stock returns.

Suggested Citation

  • BOUEZMARNI, Taoufik & VAN BELLEGEM, Sébastien, 2011. "Nonparametric Beta kernel estimator for long memory time series," LIDAM Discussion Papers CORE 2011004, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2011004
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2011.html
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    References listed on IDEAS

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    1. Pierre-Philippe Combes & Thierry Mayer & Jacques-François Thisse, 2008. "Economic Geography: The Integration of Regions and Nations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00311000, HAL.
    2. Ignacio N. Lobato & Peter M. Robinson, 1998. "A Nonparametric Test for I(0)," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 475-495.
    3. Lobato, Ignacio N & Savin, N E, 1998. "Real and Spurious Long-Memory Properties of Stock-Market Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 261-268, July.
    4. Marc Henry, 2007. "Bandwidth Choice, Optimal Rates and Adaptivity in Semiparametric Estimation of Long Memory," Springer Books, in: Gilles Teyssière & Alan P. Kirman (ed.), Long Memory in Economics, pages 157-172, Springer.
    5. Huriot,Jean-Marie & Thisse,Jacques-François (ed.), 2009. "Economics of Cities," Cambridge Books, Cambridge University Press, number 9780521118279, October.
    6. Gilles Teyssière & Alan P. Kirman (ed.), 2007. "Long Memory in Economics," Springer Books, Springer, number 978-3-540-34625-8, June.
    7. 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.
    8. Belleflamme,Paul & Peitz,Martin, 2015. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9781107687899.
    9. Winfried Pohlmeier & Luc Bauwens & David Veredas, 2007. "High frequency financial econometrics. Recent developments," ULB Institutional Repository 2013/136223, ULB -- Universite Libre de Bruxelles.
    10. Luc Bauwens & Winfried Pohlmeier & David Veredas (ed.), 2008. "High Frequency Financial Econometrics," Studies in Empirical Economics, Springer, number 978-3-7908-1992-2, October.
    11. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
    12. Lobato, Ignacio N & Velasco, Carlos, 2000. "Long Memory in Stock-Market Trading Volume," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(4), pages 410-427, October.
    13. Lobato, Ignacio N & Savin, N E, 1998. "Real and Spurious Long-Memory Properties of Stock-Market Data: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 280-283, July.
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    Cited by:

    1. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    2. Karine Bertin & Nicolas Klutchnikoff, 2014. "Adaptive Estimation of a Density Function using Beta Kernels," Working Papers 2014-08, Center for Research in Economics and Statistics.

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    More about this item

    Keywords

    spectral density; long range dependence; nonparametric estimation; periodogram; kernel smoothing; Beta kernel; cross-validation;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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