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Bootstrap autoregressive order selection

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  • Franke Jürgen
  • Kreiss Jens-Peter
  • Moser Martin

Abstract

In this paper we deal with the problem of fitting an autoregression of order p to given data coming from a stationary autoregressive process with infinite order. The paper is mainly concerned with the selection of an appropriate order of the autoregressive model. Based on the so–called final prediction error (FPE) a bootstrap order selection can be proposed, because it turns out that one relevant expression occurring in the FPE is ready for the application of the bootstrap principle. Some asymptotic properties of the bootstrap order selection are proved. To carry through the bootstrap procedure an autoregression with increasing but non–stochastic order is fitted to the given data. The paper is concluded by some simulations.

Suggested Citation

  • Franke Jürgen & Kreiss Jens-Peter & Moser Martin, 2006. "Bootstrap autoregressive order selection," Statistics & Risk Modeling, De Gruyter, vol. 24(3), pages 1-21, December.
    • Handle: RePEc:bpj:strimo:v:24:y:2006:i:3:p:21:n:1
    DOI: 10.1524/stnd.2006.24.3.305
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    References listed on IDEAS

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    1. Chen, Changhua & Davis, Richard A. & Brockwell, Peter J., 1996. "Order Determination for Multivariate Autoregressive Processes Using Resampling Methods," Journal of Multivariate Analysis, Elsevier, vol. 57(2), pages 175-190, May.
    2. E. J. Hannan & L. Kavalieris, 1986. "Regression, Autoregression Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(1), pages 27-49, January.
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