The asymptotic properties of the multichannel autoregressive spectral estimates

If we fit a-vector stationary time series using observationsx(1), ...,x(T) with AR models, then the spectral densityf() of {x(t)} can be estimated byf_k^(T)()=(2)^–A_k^(T)(e^–)^–1_k^(T)A_k^(T)(e^–i)^–, where are estimates of the variance matrix of(t), the residuals of the best linear prediction. By extending some results for the scalar case, this paper treats the asymptotic properties of the estimates in the multichannel case.