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Statistica Sinica 3(1993), 481-500



Changhua Chen, Richard A. Davis, Peter J. Brockwell and Zhi Dong Bai*

Colorado State University and Temple University*

Abstract: Let X1, ..., Xn be observations from an AR(p) model with unknown order p. A resampling procedure is proposed for estimating the order p. The classical criteria, such as AIC and BIC, estimate the order p as the minimizer of the function

where n is the sample size, k is the order of the fitted model , is an estimate of the white noise variance, and Cn is a sequence of specified constants (for AIC, Cn=2/n , for Hannan and Quinn's modification of BIC, Cn=2(lnln n)/n . Often, the traditional order selectors overfit or underfit the model for a given realization. To overcome this defect, a resampling scheme is proposed to estimate a suitable penalty factor Cn. Conditional on the data, this procedure produces a consistent estimate of p. Simulation results support the effectiveness of the procedure when compared with some of the traditional order selection criteria for both Gaussian and a range of non-Gaussian processes. A discussion of the merits of Yule-Walker estimation relative to Burg and maximum likelihood estimation for order determination is also given.

Key words and phrases: Autoregressive processes, order determination, AIC, Yule-Walker estimation, resampling.

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