Large sample identification and spectral estimation of noisy multivariate autoregressive processes

When large samples are available, identification and spectral estimation problems of a noisy multivariate autoregressive process are solved independently of the probability law governing the observed data. The procedure of solving the problems is divided into 1) estimate parameters by solving pertinent block Toeplitz and Hankel matrices as well as compute the modified Akaike information criterion for an assumed order 2) select the order and the parameter estimators corresponding to the ones which minimize the criterion function 3) compute the asymptotic distribution functions of the parameter estimators, 4) estimate power spectral density functions and coherency spectra, 5) compute the estimate confidence bounds. These five steps are numerically very efficient because the matrix equations related to block Hankel and Toeplitz matrices are well studied in the literature. The procedure is also robust because it is independent of the probability law governing the observed data.