Abstract
This paper investigates the statistical properties of multivariate autoregressive (AR) spectral analysis. Under the assumption that the data are taken from a pure multivariate AR process, we first derive the asymptotic error covariances of the elements of the estimated AR coefficient matrices and residual covariance matrix by using the periodogram technique. Next, the similar analysis is performed to obtain the error covariances of the elements of the estimated spectral density matrix.
If the order of the fitted autoregression is much greater than the true order, the covariances are similar to those of the multivariate version of the classical Blackman-Tukey method. To see the validity of the present analysis, simulation results are also shown.
