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Bootstrapping Whittle estimators

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  • 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.
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    File URL: http://hdl.handle.net/10.1093/biomet/asac044
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    References listed on IDEAS

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    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.
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