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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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    Cited by:

    1. Ronchetti, Elvezio, 2020. "Accurate and robust inference," Econometrics and Statistics, Elsevier, vol. 14(C), pages 74-88.
    2. 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.
    3. Peter C. B. Phillips, 2021. "Pitfalls in Bootstrapping Spurious Regression," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 163-217, December.
    4. La Vecchia, Davide & Ronchetti, Elvezio, 2019. "Saddlepoint approximations for short and long memory time series: A frequency domain approach," Journal of Econometrics, Elsevier, vol. 213(2), pages 578-592.
    5. Arteche, Josu & Orbe, Jesus, 2017. "A strategy for optimal bandwidth selection in Local Whittle estimation," Econometrics and Statistics, Elsevier, vol. 4(C), pages 3-17.
    6. J -P Kreiss & E Paparoditis, 2023. "Bootstrapping Whittle estimators," Biometrika, Biometrika Trust, vol. 110(2), pages 499-518.
    7. Kang, Taegyu & Kim, Young Min & Im, Jongho, 2021. "A note on stationary bootstrap variance estimator under long-range dependence," Statistics & Probability Letters, Elsevier, vol. 169(C).
    8. 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.
    9. Mikkel Bennedsen, 2016. "Semiparametric inference on the fractal index of Gaussian and conditionally Gaussian time series data," Papers 1608.01895, arXiv.org, revised Mar 2018.
    10. Arteche González, Jesús María, 2020. "Frequency Domain Local Bootstrap in long memory time series," BILTOKI info:eu-repo/grantAgreeme, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).

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