IDEAS home Printed from https://ideas.repec.org/p/rdg/emxxdp/em-dp2013-02.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: http://www.reading.ac.uk/web/FILES/economics/emdp2013099.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. K. D. Patterson, 2007. "Bias Reduction through First-order Mean Correction, Bootstrapping and Recursive Mean Adjustment," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(1), pages 23-45.
    2. Clifford M. Hurvich & Rohit S. Deo, 1999. "Plug‐in Selection of the Number of Frequencies in Regression Estimates of the Memory Parameter of a Long‐memory Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(3), pages 331-341, May.
    3. Robinson, P.M., 2005. "The distance between rival nonstationary fractional processes," Journal of Econometrics, Elsevier, vol. 128(2), pages 283-300, October.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Marc Henry, 2001. "Robust Automatic Bandwidth for Long Memory," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(3), pages 293-316, May.
    9. Arteche, J. & Orbe, J., 2005. "Bootstrapping the log-periodogram regression," Economics Letters, Elsevier, vol. 86(1), pages 79-85, January.
    10. 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.
    11. Saeed Heravi & Kerry Patterson, 2005. "Optimal And Adaptive Semi‐Parametric Narrowband And Broadband And Maximum Likelihood Estimation Of The Long‐Memory Parameter For Real Exchange Rates," Manchester School, University of Manchester, vol. 73(2), pages 165-213, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:rdg:wpaper:em-dp2013-02 is not listed on IDEAS
    2. Arteche, Josu & Orbe, Jesus, 2009. "Using the bootstrap for finite sample confidence intervals of the log periodogram regression," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 1940-1953, April.
    3. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.
    4. Uwe Hassler & Marc-Oliver Pohle, 2019. "Forecasting under Long Memory and Nonstationarity," Papers 1910.08202, arXiv.org.
    5. Henryk Gurgul & Tomasz Wójtowicz, 2006. "Long-run properties of trading volume and volatility of equities listed in DJIA index," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 16(3-4), pages 29-56.
    6. D.S. Poskitt & Gael M. Martin & Simone D. Grose, 2012. "Bias Reduction of Long Memory Parameter Estimators via the Pre-filtered Sieve Bootstrap," Monash Econometrics and Business Statistics Working Papers 8/12, Monash University, Department of Econometrics and Business Statistics.
    7. Hassler, Uwe, 2011. "Estimation of fractional integration under temporal aggregation," Journal of Econometrics, Elsevier, vol. 162(2), pages 240-247, June.
    8. Arteche González, Jesús María & Orbe Lizundia, Jesús María, 2008. "Selection of the number of frequencies using bootstrap techniques in log-periodogram regression," BILTOKI 1134-8984, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    9. repec:hal:journl:peer-00815563 is not listed on IDEAS
    10. Hassler, U. & Marmol, F. & Velasco, C., 2006. "Residual log-periodogram inference for long-run relationships," Journal of Econometrics, Elsevier, vol. 130(1), pages 165-207, January.
    11. Ana Pérez & Esther Ruiz, 2002. "Modelos de memoria larga para series económicas y financieras," Investigaciones Economicas, Fundación SEPI, vol. 26(3), pages 395-445, September.
    12. Zied Ftiti & Slim Chaouachi, 2018. "What Can We Learn About the Real Exchange Rate Behavior in the Case of a Peripheral Country?," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 16(3), pages 681-707, September.
    13. Davidson, James & Sibbertsen, Philipp, 2009. "Tests of bias in log-periodogram regression," Economics Letters, Elsevier, vol. 102(2), pages 83-86, February.
    14. Morten Ørregaard Nielsen & Per Houmann Frederiksen, 2005. "Finite Sample Comparison of Parametric, Semiparametric, and Wavelet Estimators of Fractional Integration," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 405-443.
    15. Masaki Narukawa & Yasumasa Matsuda, 2008. "Broadband semiparametric estimation of the long-memory parameter by the likelihood-based FEXP approach," TERG Discussion Papers 239, Graduate School of Economics and Management, Tohoku University.
    16. Morana, Claudio & Beltratti, Andrea, 2004. "Structural change and long-range dependence in volatility of exchange rates: either, neither or both?," Journal of Empirical Finance, Elsevier, vol. 11(5), pages 629-658, December.
    17. repec:ebl:ecbull:v:3:y:2004:i:21:p:1-16 is not listed on IDEAS
    18. Giorgio Canarella & Stephen M. Miller, 2016. "Inflation Persistence and Structural Breaks: The Experience of Inflation Targeting Countries and the US," Working papers 2016-11, University of Connecticut, Department of Economics.
    19. Sun, Yixiao & Phillips, Peter C. B., 2003. "Nonlinear log-periodogram regression for perturbed fractional processes," Journal of Econometrics, Elsevier, vol. 115(2), pages 355-389, August.
    20. Kanchana Nadarajah & Gael M Martin & Donald S Poskitt, 2019. "Optimal Bias Correction of the Log-periodogram Estimator of the Fractional Parameter: A Jackknife Approach," Monash Econometrics and Business Statistics Working Papers 7/19, Monash University, Department of Econometrics and Business Statistics.
    21. Tomasz Wójtowicz & Henryk Gurgul, 2009. "Long memory of volatility measures in time series," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 19(1), pages 37-54.
    22. Giorgio Canarella & Stephen M Miller, 2017. "Inflation Persistence Before and After Inflation Targeting: A Fractional Integration Approach," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 43(1), pages 78-103, January.
    23. Slim Chaouachi & Zied Ftiti & Frederic Teulon, 2014. "Explaining the Tunisian Real Exchange: Long Memory versus Structural Breaks," Working Papers 2014-147, Department of Research, Ipag Business School.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:rdg:emxxdp:em-dp2013-02. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Alexander Mihailov (email available below). General contact details of provider: https://edirc.repec.org/data/derdguk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.