THE ASYMPTOTIC PROPERTIES OF THE MULTICHANNEL AUTOREGRESSIVE SPECTRAL ESTIMATES

If we fit a r-vector stationary time series using observations x(1),…,x(T) with AR models x(t)+a_k~(T)(1)x(t-1)+…+a_k~(T)(k)x(t-k)=ε(t),then the spectral density f(λ) of {x(t)} can be estimated by f_k~(T)(λ)=(2π)~(-1)A_k~(T)(e~(-6λ))~(-1)Σ_k~(T) A_k~(T)(e~(-tλ))~(-k),are estimates of the variance matrix Σ of ε(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.