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Local polynomial Whittle estimation of perturbed fractional processes

Author

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  • Per Frederiksen
  • Frank S. Nielsen
  • Morten Ørregaard Nielsen

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

Abstract

We propose a semiparametric local polynomial Whittle with noise (LPWN) estimator of the memory parameter in long memory time series perturbed by a noise term which may be serially correlated. The estimator approximates the spectrum of the perturbation as well as that of the short-memory component of the signal by two separate polynomials. Furthermore, an empirical investigation of the 30 DJIA stocks shows that this estimator indicates stronger persistence in volatility than the standard local Whittle estimator.

Suggested Citation

  • Per Frederiksen & Frank S. Nielsen & Morten Ørregaard Nielsen, 2008. "Local polynomial Whittle estimation of perturbed fractional processes," CREATES Research Papers 2008-29, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2008-29
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    References listed on IDEAS

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    Cited by:

    1. de Truchis, Gilles & Keddad, Benjamin, 2016. "On the risk comovements between the crude oil market and U.S. dollar exchange rates," Economic Modelling, Elsevier, vol. 52(PA), pages 206-215.
    2. Marcel Aloy & Gilles Truchis, 2016. "Optimal Estimation Strategies for Bivariate Fractional Cointegration Systems and the Co-persistence Analysis of Stock Market Realized Volatilities," Computational Economics, Springer;Society for Computational Economics, vol. 48(1), pages 83-104, June.
    3. Per Frederiksen & Morten Orregaard Nielsen, 2008. "Bias-Reduced Estimation of Long-Memory Stochastic Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(4), pages 496-512, Fall.
    4. Eduardo Rossi & Paolo Santucci de Magistris, 2014. "Estimation of Long Memory in Integrated Variance," Econometric Reviews, Taylor & Francis Journals, vol. 33(7), pages 785-814, October.
    5. Shi, Wendong & Sun, Jingwei, 2016. "Aggregation and long-memory: An analysis based on the discrete Fourier transform," Economic Modelling, Elsevier, vol. 53(C), pages 470-476.
    6. Leschinski, Christian, 2017. "On the memory of products of long range dependent time series," Economics Letters, Elsevier, vol. 153(C), pages 72-76.
    7. Robinson Kruse & Christian Leschinski & Michael Will, 2016. "Comparing Predictive Accuracy under Long Memory - With an Application to Volatility Forecasting," CREATES Research Papers 2016-17, Department of Economics and Business Economics, Aarhus University.
    8. Torben G. Andersen & Rasmus T. Varneskov, 2702. "Consistent Inference for Predictive Regressions in Persistent VAR Economies," CREATES Research Papers 2018-09, Department of Economics and Business Economics, Aarhus University.
    9. Wenger, Kai & Leschinski, Christian & Sibbertsen, Philipp, 2017. "The Memory of Volatility," Hannover Economic Papers (HEP) dp-601, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    10. Busch, Marie & Sibbertsen, Philipp, 2018. "An Overview of Modified Semiparametric Memory Estimation Methods," Hannover Economic Papers (HEP) dp-628, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    11. Stelios Arvanitis & Antonis Demos, "undated". "A Class of Indirect Inference Estimators: Higher Order Asymptotics and Approximate Bias Correction (Revised)," DEOS Working Papers 1411, Athens University of Economics and Business, revised 23 Sep 2014.
    12. repec:gam:jecnmx:v:6:y:2018:i:1:p:13-:d:135826 is not listed on IDEAS
    13. Arteche, Josu & Orbe, Jesus, 2016. "A bootstrap approximation for the distribution of the Local Whittle estimator," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 645-660.
    14. Mccloskey, Adam & Perron, Pierre, 2013. "Memory Parameter Estimation In The Presence Of Level Shifts And Deterministic Trends," Econometric Theory, Cambridge University Press, vol. 29(06), pages 1196-1237, December.
    15. Hou, Jie & Perron, Pierre, 2014. "Modified local Whittle estimator for long memory processes in the presence of low frequency (and other) contaminations," Journal of Econometrics, Elsevier, vol. 182(2), pages 309-328.
    16. 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.
    17. Frank S. Nielsen, 2008. "Local polynomial Whittle estimation covering non-stationary fractional processes," CREATES Research Papers 2008-28, Department of Economics and Business Economics, Aarhus University.

    More about this item

    Keywords

    Bias reduction; local Whittle; long memory; perturbed fractional process; semiparametric estimation; stochastic volatility;

    JEL classification:

    • 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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