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Wavelet Estimation of Gegenbauer Processes: Simulation and Empirical Application

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  • Heni Boubaker

Abstract

The aim of this paper is to estimate the parameters of a stationary Gegenbauer process using a wavelet methodology where the selection of the orthonormal basis is given by generalized variance portmanteau test. Two other maximum likelihood estimators, including the Whittle and the wavelets—Whitcher (Technometrics 46:225–238, 2004 ) estimators, are also considered. We have shown by Monte-Carlo experiments that the new selection procedure improves considerably the Whittle and Whitcher estimators. Moreover, to assess the impact of volatility in the estimation methods, we assumed that the innovations $$\varepsilon _{t}$$ ε t are generated by univariate GARCH process. Simulation experiments show that the wavelets estimators perform better under most situations than the Whittle estimator. We then applied this new selection method to the consumer price index in monthly frequencies for the United States and find that this is more appropriate for forecasts. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Heni Boubaker, 2015. "Wavelet Estimation of Gegenbauer Processes: Simulation and Empirical Application," Computational Economics, Springer;Society for Computational Economics, vol. 46(4), pages 551-574, December.
    • Handle: RePEc:kap:compec:v:46:y:2015:i:4:p:551-574
    DOI: 10.1007/s10614-014-9471-6
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    References listed on IDEAS

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    1. Collet J.J. & Fadili J.M., 2005. "Simulation of Gegenbauer processes using wavelet packets," School of Economics and Finance Discussion Papers and Working Papers Series 190, School of Economics and Finance, Queensland University of Technology.
    2. Boubaker Heni & Boutahar Mohamed, 2011. "A wavelet-based approach for modelling exchange rates," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 20(2), pages 201-220, June.
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    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
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    6. Heni Boubaker & Anne Péguin-Feissolle, 2013. "Estimating the Long-Memory Parameter in Nonstationary Processes Using Wavelets," Computational Economics, Springer;Society for Computational Economics, vol. 42(3), pages 291-306, October.
    7. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    8. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    9. Esam Mahdi & A. Ian McLeod, 2012. "Improved multivariate portmanteau test," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(2), pages 211-222, March.
    10. Henry L. Gray & Nien‐Fan Zhang & Wayne A. Woodward, 1989. "On Generalized Fractional Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(3), pages 233-257, May.
    11. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
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    Cited by:

    1. Fan He & Xuansen He, 2019. "A Continuous Differentiable Wavelet Shrinkage Function for Economic Data Denoising," Computational Economics, Springer;Society for Computational Economics, vol. 54(2), pages 729-761, August.
    2. Souhir Ben Amor & Heni Boubaker & Lotfi Belkacem, 2022. "A Dual Generalized Long Memory Modelling for Forecasting Electricity Spot Price: Neural Network and Wavelet Estimate," Papers 2204.08289, arXiv.org.
    3. Yixun Xing & Wayne A. Woodward, 2021. "R-Squared-Bootstrapping for Gegenbauer-Type Long Memory," Computational Economics, Springer;Society for Computational Economics, vol. 57(2), pages 773-790, February.
    4. Richard Hunt & Shelton Peiris & Neville Weber, 2022. "Estimation methods for stationary Gegenbauer processes," Statistical Papers, Springer, vol. 63(6), pages 1707-1741, December.

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    More about this item

    Keywords

    Gegenbauer process; Wavelet analysis; Generalized variance portmanteau test; Heteroskedasticity; Monte-Carlo simulation; CPI; C13; C15; C22;
    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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