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Wavelet Estimation Performance of Fractional Integrated Processes with Heavy-Tails

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  • Heni Boubaker

    (Technopolis Rabat-Shore)

Abstract

In this paper, we investigate the performance of four semi-parametric estimators in the wavelet domain in order to estimate the parameter of stationary long-memory models. The goal is to consider a wavelet estimate for the fractional differencing parameter d where the time series exhibit heavy tails. We show by Monte Carlo experiments that the wavelet Exact Local Whittle-type estimator improves considerably the other suggested wavelet-based estimators in terms of smaller bias, Root Mean Squared Error and variance. Furthermore, the simulation results show that the wavelet periodogram estimators perform better in most cases than wavelet ordinary least square estimate methods when the sample size is increased.

Suggested Citation

  • 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.
    • Handle: RePEc:kap:compec:v:55:y:2020:i:2:d:10.1007_s10614-019-09897-9
    DOI: 10.1007/s10614-019-09897-9
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    References listed on IDEAS

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    1. Agnieszka Jach & Piotr Kokoszka, 2010. "Robust Wavelet-Domain Estimation of the Fractional Difference Parameter in Heavy-Tailed Time Series: An Empirical Study," Methodology and Computing in Applied Probability, Springer, vol. 12(1), pages 177-197, March.
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    3. Heni Boubaker & Anne Peguin-Feissolle, 2013. "Estimating the Long-Memory Parameter in Nonstationary Processes Using Wavelets," Post-Print hal-01498239, HAL.
    4. John Geweke & Susan Porter‐Hudak, 1983. "The Estimation And Application Of Long Memory Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(4), pages 221-238, July.
    5. Donald W. K. Andrews & Patrik Guggenberger, 2003. "A Bias--Reduced Log--Periodogram Regression Estimator for the Long--Memory Parameter," Econometrica, Econometric Society, vol. 71(2), pages 675-712, March.
    6. Mark J. Jensen, 1997. "Using Wavelets to Obtain a Consistent Ordinary Least Squares Estimator of the Long Memory Parameter," Econometrics 9710002, University Library of Munich, Germany.
    7. Lee, Jin, 2005. "Estimating memory parameter in the US inflation rate," Economics Letters, Elsevier, vol. 87(2), pages 207-210, May.
    8. Kokoszka, Piotr S. & Taqqu, Murad S., 1995. "Fractional ARIMA with stable innovations," Stochastic Processes and their Applications, Elsevier, vol. 60(1), pages 19-47, November.
    9. Patrick M. Crowley, 2007. "A Guide To Wavelets For Economists," Journal of Economic Surveys, Wiley Blackwell, vol. 21(2), pages 207-267, April.
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    Cited by:

    1. Long Hai Vo & Duc Hong Vo, 2020. "Modelling Australian Dollar Volatility at Multiple Horizons with High-Frequency Data," Risks, MDPI, vol. 8(3), pages 1-16, August.

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    More about this item

    Keywords

    Long-memory; Wavelet estimation; Heavy tails; Stable distributions; Monte Carlo simulation;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: 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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