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Log-Periodogram Estimation of the Long-Memory Parameter: An Evaluation of Competing Estimators

Author

Listed:
  • Saeed Heravi

    (Cardiff Business School, University of Wales)

  • Kerry Patterson

    (Department of Economics, University of Reading)

Abstract

This study evaluates a number of methods of reducing the bias and mean squared error of log-periodogram (LP) based methods to estimate the long-memory parameter and, in addition, assesses the actual coverage of the associated confidence intervals, considering both tails and the width of the interval. This is critical as previous results concentrating on two-sided intervals may mask severe distortion in one tail. The evaluation includes: developments of the Geweke and Porter-Hudak (GPH) method due to Hurvich and Deo (1999) and Andrews and Guggenberger (AG, 2003); the weighted LP, WLP, estimator due to Guggenberger and Sun (GS, 2004, 2006); and a frequency-based bootstrap method to improve estimator performance. A central problem in the application of these methods is the selection of the number of frequencies, m, to be included in the LP regression. A frequently used, but generally unsatisfactory, solution is to use a fixed number of frequencies of the form m = n^alpha where, for example, alpha = 0.5 (the square-root rule) or 0.7; in contrast we use a plug-in method to obtain a feasible first-order bias reduced estimator. Including infeasible, feasible and bootstrapped variations, 11 estimators are considered and the simulations suggest that whilst there is no single dominant estimation method, the bootstrapped versions associated with each method generally offer significant gains over the standard versions for coverage rate accuracy. Overall, the bootstrapped WLP estimator is superior for 'moderate' serial correlation in the short-run dynamics and offers a significant reduction in the average width of the confidence intervals. The results are illustrated with data on the Nile river flow and the gold-silver price.

Suggested Citation

  • Saeed Heravi & Kerry Patterson, 2013. "Log-Periodogram Estimation of the Long-Memory Parameter: An Evaluation of Competing Estimators," Economics Discussion Papers em-dp2013-02, Department of Economics, University of Reading.
    • Handle: RePEc:rdg:emxxdp:em-dp2013-02
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    File URL: http://www.reading.ac.uk/web/FILES/economics/emdp2013099.pdf
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    References listed on IDEAS

    as
    1. Sowell, Fallaw, 1992. "Maximum likelihood estimation of stationary univariate fractionally integrated time series models," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 165-188.
    2. Guggenberger, Patrik & Sun, Yixiao, 2006. "Bias-Reduced Log-Periodogram And Whittle Estimation Of The Long-Memory Parameter Without Variance Inflation," Econometric Theory, Cambridge University Press, vol. 22(5), pages 863-912, October.
    3. 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.
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    6. 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.
    7. Christos Agiakloglou & Paul Newbold & Mark Wohar, 1993. "Bias In An Estimator Of The Fractional Difference Parameter," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(3), pages 235-246, May.
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    More about this item

    Keywords

    Long memory; bootstrapb log-periodogram regression; weighted LP regression;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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