ON THE COVARIANCE-MATRIX ESTIMATORS OF THE WHITE-NOISE PROCESS OF A VECTOR AUTOREGRESSIVE MODEL

The penalty function identification methods such as the AIC, the CAT, the BIC and Hannan and Quinn's criterion have been used to determine the order of a vector autoregressive model. To use the methods, it is necessary to calculate the maximum likelihood estimates of the covariance matrices of the white noise processes of several vector autoregressive models. Since the maximum likelihood estimation needs a lot of calculation, the Yule-Walker estimators of the white noise covariance matrices are used instead. In this paper the biases of the maximum likelihood estimator and the Yule-Walker estimator of the white noise covariance matrix are derived up to O(1/T2), where T is the number of observations. Also, new estimators based on either the maximum likelihood estimator or the Yule-Walker estimator, which are less biased than the original ones, are proposed to identify the vector autoregressive model more adequately through the penalty function identification methods.