Order Determination for Multivariate Autoregressive Processes Using Resampling Methods

Author： Chen C. Davis R.A. Brockwell P.J.

ISSN： 0047-259X

Source： Journal of Multivariate Analysis, Vol.57, Iss.2, 1996-05, pp. : 175-190

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Abstract

Let X 1 , , X n be observations from a multivariate 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 delta(k)=ln (left| hat{Sigma}right| )+C_n k where n is the sample size, k is the order of the fitted model, ^Sigma 2 k is an estimate of the white noise covariance matrix, and C n is a sequence of specified constants (for AIC, C n =2 m 2 / n , for Hannan and Quinn's modification of BIC, C n =2 m 2 (ln ln n )/ n , where m is the dimension of the data vector). A resampling scheme is proposed to estimate an improved penalty factor C n . Conditional on the data, this procedure produces a consistent estimate of p . 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.