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Order Determination for Multivariate Autoregressive Processes Using Resampling Methods


  • Chen, Changhua
  • Davis, Richard A.
  • Brockwell, Peter J.


LetX1, ..., Xnbe observations from a multivariate AR(p) model with unknown orderp. A resampling procedure is proposed for estimating the orderp. The classical criteria, such as AIC and BIC, estimate the orderpas the minimizer of the function[formula]wherenis the sample size,kis the order of the fitted model, [Sigma]2kis an estimate of the white noise covariance matrix, andCnis a sequence of specified constants (for AIC,Cn=2m2/n, for Hannan and Quinn's modification of BIC,Cn=2m2(ln ln n)/n, wheremis the dimension of the data vector). A resampling scheme is proposed to estimate an improved penalty factorCn. Conditional on the data, this procedure produces a consistent estimate ofp. Simulation results support the effectiveness of this procedure when compared with some of the traditional order selection criteria. Comments are also made on the use of Yule-Walker as opposed to conditional least squares estimations for order selection.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:jmvana:v:57:y:1996:i:2:p:175-190

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    Cited by:

    1. Franke Jürgen & Kreiss Jens-Peter & Moser Martin, 2006. "Bootstrap autoregressive order selection," Statistics & Risk Modeling, De Gruyter, vol. 24(3), pages 1-21, December.
    2. Pappas, S.Sp. & Ekonomou, L. & Karamousantas, D.Ch. & Chatzarakis, G.E. & Katsikas, S.K. & Liatsis, P., 2008. "Electricity demand loads modeling using AutoRegressive Moving Average (ARMA) models," Energy, Elsevier, vol. 33(9), pages 1353-1360.
    3. Hsu, Nan-Jung & Hung, Hung-Lin & Chang, Ya-Mei, 2008. "Subset selection for vector autoregressive processes using Lasso," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3645-3657, March.


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