ORDER DETERMINATION FOR MULTIVARIATE AUTOREGRESSIVE PROCESSES USING RESAMPLING METHODS

Let X(1),..., X(n) be observations from a multivariate AR(p) model wit h unknown order p. A resampling procedure is proposed for estimating t he order p. The classical criteria, such as AIC and BIC, estimate the order p as the minimizer of the function delta(k) = ln (\<(Sigma)over cap>(k)\) + C(n)k where n is the sample size, k is the order of the fi tted model, <(Sigma)over cap>(2)(k) is an estimate of the white noise covariance matrix, and C-n is a sequence of specified constants (for A IC, C-n = 2m(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 resam pling scheme is proposed to estimate an improved penalty factor C-n. C onditional on the data, this procedure produces a consistent estimate of p. Simulation results support the effectiveness of this procedure w hen compared with some of the traditional order selection criteria. Co mments are also made on the use of Yule-Walker as opposed to condition al least squares estimations for order selection. (C) 1996 Academic Pr ess, Inc.