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Wavelet transform for log periodogram regression in long memory stochastic volatility model

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  • Jin Lee

Abstract

We consider semiparametric log periodogram regression estimation of memory parameter for the latent process in long memory stochastic volatility models. It is known that though widely used among researchers, the Geweke and Porter-Hudak (1983; GPH) LP estimator violates the Gaussian or Martingale assumption, which results in significant negative bias due to the existence of the spectrum of non-Gaussian noise. Through wavelet transform of the squared process, we effectively remove the noise spectrum around zero frequency, and obtain Gaussian-approximate spectral representation at zero frequency. We propose wavelet-based regression estimator, and derive the asymptotic mean squared error and the consistency in line with the asymptotic theory in the long memory literature. Simulation studies show that wavelet-based regression estimation is an effective way in reducing the bias, compared with the GPH estimator

Suggested Citation

  • Jin Lee, 2004. "Wavelet transform for log periodogram regression in long memory stochastic volatility model," Econometric Society 2004 Far Eastern Meetings 682, Econometric Society.
    • Handle: RePEc:ecm:feam04:682
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    References listed on IDEAS

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    1. 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.
    2. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
    3. Clifford M. Hurvich & Rohit Deo & Julia Brodsky, 1998. "The mean squared error of Geweke and Porter‐Hudak's estimator of the memory parameter of a long‐memory time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(1), pages 19-46, January.
    4. Takeshi Kato & Elias Masry, 1999. "On the Spectral Density of the Wavelet Transform of Fractional Brownian Motion," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(5), pages 559-563, September.
    5. Shimotsu, Katsumi & Phillips, Peter C B, 2002. "Exact Local Whittle Estimation of Fractional Integration," Economics Discussion Papers 8838, University of Essex, Department of Economics.
    6. Deo, Rohit S. & Hurvich, Clifford M., 2001. "On The Log Periodogram Regression Estimator Of The Memory Parameter In Long Memory Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 17(4), pages 686-710, August.
    7. Bollerslev, Tim & Wright, Jonathan H., 2000. "Semiparametric estimation of long-memory volatility dependencies: The role of high-frequency data," Journal of Econometrics, Elsevier, vol. 98(1), pages 81-106, September.
    8. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(4), pages 549-582, August.
    9. Phillips, Peter C.B., 2007. "Unit root log periodogram regression," Journal of Econometrics, Elsevier, vol. 138(1), pages 104-124, May.
    10. Jin Lee, 2004. "Wavelet transform for regression estimation of non-stationary fractional time series," Econometric Society 2004 North American Summer Meetings 491, Econometric Society.
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    More about this item

    Keywords

    Long memory stochastic volatility; Wavelet transform; Log periodogram regression;
    All these keywords.

    JEL classification:

    • 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

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