IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v110y2023i2p499-518..html
   My bibliography  Save this article

Bootstrapping Whittle estimators

Author

Listed:
  • J -P Kreiss
  • E Paparoditis

Abstract

SummaryFitting parametric models by optimizing frequency-domain objective functions is an attractive approach of parameter estimation in time series analysis. Whittle estimators are a prominent example in this context. Under weak conditions and the assumption that the true spectral density of the underlying process does not necessarily belong to the parametric class of spectral densities fitted, the distribution of Whittle estimators typically depends on difficult to estimate characteristics of the underlying process. This makes the implementation of asymptotic results for the construction of confidence intervals or for assessing the variability of estimators difficult in practice. In this paper we propose a frequency-domain bootstrap method to estimate the distribution of Whittle estimators that is asymptotically valid under assumptions that not only allow for possible model misspecification, but also for weak dependence conditions that are satisfied by a wide range of stationary stochastic processes. Adaptations of the bootstrap procedure developed to incorporate different modifications of Whittle estimators proposed in the literature, such as, for instance, tapered, debiased or boundary extended Whittle estimators, are also considered. Simulations demonstrate the capabilities of the bootstrap method proposed and its good finite sample performance. A real-life data analysis on sunspots is also presented.

Suggested Citation

  • J -P Kreiss & E Paparoditis, 2023. "Bootstrapping Whittle estimators," Biometrika, Biometrika Trust, vol. 110(2), pages 499-518.
    • Handle: RePEc:oup:biomet:v:110:y:2023:i:2:p:499-518.
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/biomet/asac044
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

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

    References listed on IDEAS

    as
    1. Shao, Xiaofeng, 2010. "Nonstationarity-Extended Whittle Estimation," Econometric Theory, Cambridge University Press, vol. 26(4), pages 1060-1087, August.
    2. Robinson, P M, 1991. "Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models," Econometrica, Econometric Society, vol. 59(5), pages 1329-1363, September.
    3. Efstathios Paparoditis & Dimitris N. Politis, 1999. "The Local Bootstrap for Periodogram Statistics," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(2), pages 193-222, March.
    4. 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.
    5. Adam M Sykulski & Sofia C Olhede & Arthur P Guillaumin & Jonathan M Lilly & Jeffrey J Early, 2019. "The debiased Whittle likelihood," Biometrika, Biometrika Trust, vol. 106(2), pages 251-266.
    6. Robinson, Peter M. & Velasco, Carlos, 2000. "Whittle pseudo-maximum likelihood estimation for nonstationary time series," LSE Research Online Documents on Economics 2273, London School of Economics and Political Science, LSE Library.
    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. de Truchis, Gilles, 2013. "Approximate Whittle analysis of fractional cointegration and the stock market synchronization issue," Economic Modelling, Elsevier, vol. 34(C), pages 98-105.
    2. Peter C. B. Phillips, 2023. "Discrete Fourier Transforms of Fractional Processes with Econometric Applications," Advances in Econometrics, in: Essays in Honor of Joon Y. Park: Econometric Theory, volume 45, pages 3-71, Emerald Group Publishing Limited.
    3. Robinson, Peter M. & Hualde, Javier, 2003. "Cointegration in fractional systems with unknown integration orders," LSE Research Online Documents on Economics 2223, London School of Economics and Political Science, LSE Library.
    4. Cheung, Ying Lun, 2020. "Nonstationarity-extended Whittle estimation with discontinuity: A correction," Economics Letters, Elsevier, vol. 187(C).
    5. Ying Lun Cheung & Uwe Hassler, 2020. "Whittle-type estimation under long memory and nonstationarity," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(3), pages 363-383, September.
    6. Arteche, Josu, 2024. "Bootstrapping long memory time series: Application in low frequency estimators," Econometrics and Statistics, Elsevier, vol. 29(C), pages 1-15.
    7. 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.
    8. 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.
    9. 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.
    10. Xiaofei Xu & Yan Liu & Masanobu Taniguchi, 2023. "Higher‐order asymptotics of minimax estimators for time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(2), pages 247-257, March.
    11. repec:ehu:biltok:48980 is not listed on IDEAS
    12. Morten Ørregaard Nielsen, 2015. "Asymptotics for the Conditional-Sum-of-Squares Estimator in Multivariate Fractional Time-Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 154-188, March.
    13. Chambers, Marcus J. & Ercolani, Joanne S. & Taylor, A.M. Robert, 2014. "Testing for seasonal unit roots by frequency domain regression," Journal of Econometrics, Elsevier, vol. 178(P2), pages 243-258.
    14. Wouter J. Den Haan & Andrew T. Levin, 1995. "Inferences from parametric and non-parametric covariance matrix estimation procedures," International Finance Discussion Papers 504, Board of Governors of the Federal Reserve System (U.S.).
    15. Bunzel, Helle, 2006. "FIXED-b ASYMPTOTICS IN SINGLE-EQUATION COINTEGRATION MODELS WITH ENDOGENOUS REGRESSORS," Econometric Theory, Cambridge University Press, vol. 22(4), pages 743-755, August.
    16. Guglielmo Caporale & Luis Gil-Alana, 2014. "Fractional integration and cointegration in US financial time series data," Empirical Economics, Springer, vol. 47(4), pages 1389-1410, December.
    17. Yuliya Lovcha & Alejandro Perez-Laborda, 2017. "Structural shocks and dynamic elasticities in a long memory model of the US gasoline retail market," Empirical Economics, Springer, vol. 53(2), pages 405-422, September.
    18. Javier Hidalgo, 2003. "A Bootstrap Causality Test for Covariance Stationary Processes," STICERD - Econometrics Paper Series 462, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    19. Girard, Didier A., 2020. "Asymptotic near-efficiency of the “Gibbs-energy (GE) and empirical-variance” estimating functions for fitting Matérn models - II: Accounting for measurement errors via “conditional GE mean”," Statistics & Probability Letters, Elsevier, vol. 162(C).
    20. Laura Mayoral, 2007. "Minimum distance estimation of stationary and non-stationary ARFIMA processes," Econometrics Journal, Royal Economic Society, vol. 10(1), pages 124-148, March.
    21. Hidalgo, Javier, 2007. "Specification testing for regression models with dependent data," LSE Research Online Documents on Economics 6799, London School of Economics and Political Science, LSE Library.

    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:oup:biomet:v:110:y:2023:i:2:p:499-518.. 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: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/biomet .

    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.