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Estimating the Long-Memory Parameter in Nonstationary Processes Using Wavelets

Author

Listed:
  • Heni Boubaker

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • Anne Peguin-Feissolle

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this article, we propose two new semiparametric estimators in the wavelet domain in order to estimate the parameter of nonstationary long memory models. Compared to the Fourier transform, the advantage of the wavelet approach to analyze the behavior of nonstationary time series is that it can localize a process simultaneously in time and scale. We thus develop a Wavelet Exact Local Whittle estimator and a Wavelet Feasible Exact Local Whittle estimator, which extend the estimators of Phillips and Shimotsu (Ann Stat 32(2):656–692, 2004 ), Shimotsu and Phillips (Ann Stat 33(4):1890–1933, 2005 ; J Econom 130:209–233, 2006 ) and Shimotsu (Econom Theory 26(2):501–540, 2010 ) into the wavelet domain. Simulation experiments show that the new estimators perform better under most situations in the stationary and nonstationary cases. We also applied these two new semiparametric estimators to some financial series (daily stock market indices and exchange rates). Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Heni Boubaker & Anne Peguin-Feissolle, 2013. "Estimating the Long-Memory Parameter in Nonstationary Processes Using Wavelets," Post-Print hal-01498239, HAL.
    • Handle: RePEc:hal:journl:hal-01498239
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    Citations

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    Cited by:

    1. Bhandari, Avishek, 2020. "Long Memory and Correlation Structures of Select Stock Returns Using Novel Wavelet and Fractal Connectivity Networks," MPRA Paper 101946, University Library of Munich, Germany.
    2. Heni Boubaker, 2020. "Wavelet Estimation Performance of Fractional Integrated Processes with Heavy-Tails," Computational Economics, Springer;Society for Computational Economics, vol. 55(2), pages 473-498, February.
    3. Avishek Bhandari & Bandi Kamaiah, 2020. "Long memory in select stock returns using an alternative wavelet log-scale alignment approach," Papers 2004.08550, arXiv.org.
    4. Boubaker Heni & Canarella Giorgio & Gupta Rangan & Miller Stephen M., 2021. "Long-memory modeling and forecasting: evidence from the U.S. historical series of inflation," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 25(5), pages 289-310, December.
    5. Dima, Bogdan & Dima, Ştefana Maria, 2017. "Mutual information and persistence in the stochastic volatility of market returns: An emergent market example," International Review of Economics & Finance, Elsevier, vol. 51(C), pages 36-59.
    6. Bhandari, Avishek, 2020. "Long memory and fractality among global equity markets: A multivariate wavelet approach," MPRA Paper 99653, University Library of Munich, Germany.

    More about this item

    Keywords

    C13; C22; long memory; Nonstationarity; Wavelet analysis; Whittle estimation;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: 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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