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

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  • Kim, Young Min
  • Nordman, Daniel J.

Abstract

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
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    References listed on IDEAS

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    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.
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    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, arXiv.org, revised Oct 2017.
    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.

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