Statistica Sinica

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

Abstract:LetX_{1}, ...,X_{n}be observations from an 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

wherenis the sample size,kis the order of the fitted model , is an estimate of the white noise variance, andCis a sequence of specified constants (for AIC,_{n}C=2/_{n}n, for Hannan and Quinn's modification of BIC,C=2(lnln_{n}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 factorC. Conditional on the data, this procedure produces a consistent estimate of_{n}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.