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Bootstrap Methods for Time Series

Author

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  • Wolfgang Härdle
  • Joel Horowitz
  • Jens‐Peter Kreiss

Abstract

Summary The bootstrap is a method for estimating the distribution of an estimator or test statistic by resampling one's data or a model estimated from the data. The methods that are available for implementing the bootstrap and the accuracy of bootstrap estimates depend on whether the data are an independent random sample or a time series. This paper is concerned with the application of the bootstrap to time‐series data when one does not have a finite‐dimensional parametric model that reduces the data generation process to independent random sampling. We review the methods that have been proposed for implementing the bootstrap in this situation and discuss the accuracy of these methods relative to that of first‐order asymptotic approximations. We argue that methods for implementing the bootstrap with time‐series data are not as well understood as methods for data that are independent random samples. Although promising bootstrap methods for time series are available, there is a considerable need for further research in the application of the bootstrap to time series. We describe some of the important unsolved problems. Résumé Le bootstrap est une méthode pour estimer la distribution d'un estimateur en rééchantillonnant ses données ou un modéle estiméà partir des données. Les méthodes disponibles pour mettre en oeuvre le bootstrap et la précision des estimateurs de bootstrap dépendent de ce que les données proviennent d'un échantillon aléatoire indépendant ou d'une série temporelle. Cet article concerne l'application du bootstrap aux données des séries temporelles quand on ne dispose pas de modéle paramétrique de dimension finie qui réduise le processus de génération des données à l'échantillonnage aléatoire indépendent. Nous examinons les méthodes qui ont été proposées pour mettre en oeuvre le bootstrap dans cette situation et discutons la precision de ces méthodes comparativement à celle des approximations asymptotiques de premier ordre. Nous montrons que les méthodes pour mettre en oeuvre le bootstrap avec les données des séries temporelles ne sont pas aussi bien comprises que les méthodes pour les données des échantillons aléatoires indépendants. Bien que des méthodes de bootstrap prometteuses pour les séries temporelles soient disponibles, il y a un besoin considérable de recherche supplémental re dans leur application. Nous décrivons quelques problémes importants non résolus.

Suggested Citation

  • Wolfgang Härdle & Joel Horowitz & Jens‐Peter Kreiss, 2003. "Bootstrap Methods for Time Series," International Statistical Review, International Statistical Institute, vol. 71(2), pages 435-459, August.
    • Handle: RePEc:bla:istatr:v:71:y:2003:i:2:p:435-459
    DOI: 10.1111/j.1751-5823.2003.tb00485.x
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    References listed on IDEAS

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