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Bias-reduced estimation of long memory stochastic volatility

Author

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  • Per Frederiksen
  • Morten Ørregaard Nielsen

    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

Abstract

We propose to use a variant of the local polynomial Whittle estimator to estimate the memory parameter in volatility for long memory stochastic volatility models with potential nonstation- arity in the volatility process. We show that the estimator is asymptotically normal and capable of obtaining bias reduction as well as a rate of convergence arbitrarily close to the parametric rate, n1=2. A Monte Carlo study is conducted to support the theoretical results, and an analysis of daily exchange rates demonstrates the empirical usefulness of the estimators

Suggested Citation

  • Per Frederiksen & Morten Ørregaard Nielsen, 2008. "Bias-reduced estimation of long memory stochastic volatility," CREATES Research Papers 2008-35, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2008-35
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    References listed on IDEAS

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    Cited by:

    1. Frederiksen, Per & Nielsen, Frank S. & Nielsen, Morten Ørregaard, 2012. "Local polynomial Whittle estimation of perturbed fractional processes," Journal of Econometrics, Elsevier, vol. 167(2), pages 426-447.
    2. Jensen Mark J., 2016. "Robust estimation of nonstationary, fractionally integrated, autoregressive, stochastic volatility," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(4), pages 455-475, September.
    3. Artiach, Miguel & Arteche, Josu, 2012. "Doubly fractional models for dynamic heteroscedastic cycles," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2139-2158.
    4. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.
    5. Marie Busch & Philipp Sibbertsen, 2018. "An Overview of Modified Semiparametric Memory Estimation Methods," Econometrics, MDPI, vol. 6(1), pages 1-21, March.
    6. Adam McCloskey, 2012. "Estimation of the Long-Memory Stochastic Volatility Model Parameters that is Robust to Level Shifts and Deterministic Trends," Working Papers 2012-17, Brown University, Department of Economics.
    7. Adam McCloskey, 2013. "Estimation of the long-memory stochastic volatility model parameters that is robust to level shifts and deterministic trends," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(3), pages 285-301, May.
    8. Per Frederiksen & Frank S. Nielsen, 2008. "Estimation of Dynamic Models with Nonparametric Simulated Maximum Likelihood," CREATES Research Papers 2008-59, Department of Economics and Business Economics, Aarhus University.

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    More about this item

    Keywords

    Bias reduction; local Whittle estimation; long memory stochastic volatility model;
    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

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