IDEAS home Printed from
   My bibliography  Save this article

A frequency domain bootstrap for Whittle estimation under long-range dependence


  • Kim, Young Min
  • Nordman, Daniel J.


Whittle estimation is a common technique for fitting parametric spectral density functions to time series, in an effort to model the underlying covariance structure. However, Whittle estimators from long-range dependent processes can exhibit slow convergence to their Gaussian limit law so that calibrating confidence intervals with normal approximations may perform poorly. As a remedy, we study a frequency domain bootstrap (FDB) for approximating the distribution of Whittle estimators. The method provides valid distribution estimation for a broad class of stationary, long-range (or short-range) dependent linear processes, without stringent assumptions on the distribution of the underlying process. A large simulation study shows that the FDB approximations often improve normal approximations for setting confidence intervals for Whittle parameters in spectral models with strong dependence.

Suggested Citation

  • Kim, Young Min & Nordman, Daniel J., 2013. "A frequency domain bootstrap for Whittle estimation under long-range dependence," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 405-420.
  • Handle: RePEc:eee:jmvana:v:115:y:2013:i:c:p:405-420
    DOI: 10.1016/j.jmva.2012.10.018

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. Hidalgo, Javier, 2003. "An alternative bootstrap to moving blocks for time series regression models," LSE Research Online Documents on Economics 6850, London School of Economics and Political Science, LSE Library.
    2. Jentsch, Carsten & Kreiss, Jens-Peter, 2010. "The multiple hybrid bootstrap -- Resampling multivariate linear processes," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2320-2345, November.
    3. Nordman, Daniel J. & Lahiri, Soumendra N., 2005. "Validity Of The Sampling Window Method For Long-Range Dependent Linear Processes," Econometric Theory, Cambridge University Press, vol. 21(06), pages 1087-1111, December.
    4. Donald W. K. Andrews & Yixiao Sun, 2004. "Adaptive Local Polynomial Whittle Estimation of Long-range Dependence," Econometrica, Econometric Society, vol. 72(2), pages 569-614, March.
    5. Andrews, Donald W.K. & Lieberman, Offer & Marmer, Vadim, 2006. "Higher-order improvements of the parametric bootstrap for long-memory Gaussian processes," Journal of Econometrics, Elsevier, vol. 133(2), pages 673-702, August.
    6. Javier Hidalgo, 2003. "An Alternative Bootstrap to Moving Blocks for Time Series Regression Models," STICERD - Econometrics Paper Series 452, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    7. Hidalgo, Javier, 2003. "An alternative bootstrap to moving blocks for time series regression models," Journal of Econometrics, Elsevier, vol. 117(2), pages 369-399, December.
    8. George Kapetanios & Zacharias Psaradakis, 2006. "Sieve Bootstrap for Strongly Dependent Stationary Processes," Working Papers 552, Queen Mary University of London, School of Economics and Finance.
    9. Kang, Sang Hoon & Yoon, Seong-Min, 2007. "Long memory properties in return and volatility: Evidence from the Korean stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 591-600.
    10. Lahiri, S. N., 1993. "On the moving block bootstrap under long range dependence," Statistics & Probability Letters, Elsevier, vol. 18(5), pages 405-413, December.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. 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.
    2. repec:eee:ecosta:v:4:y:2017:i:c:p:3-17 is not listed on IDEAS
    3. Mikkel Bennedsen, 2016. "Semiparametric inference on the fractal index of Gaussian and conditionally Gaussian time series data," Papers 1608.01895,, revised Mar 2018.
    4. Mikkel Bennedsen, 2016. "Semiparametric inference on the fractal index of Gaussian and conditionally Gaussian time series data," CREATES Research Papers 2016-21, Department of Economics and Business Economics, Aarhus University.


    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:eee:jmvana:v:115:y:2013:i:c:p:405-420. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.