THE LIMIT PROCESS OF WEIGHTED SPECTRAL ESTIMATES FOR A MULTIPLE STATIONARY GAUSSIAN PROCESS

Let X(t) = (X1(t), X2(t), • •• , Xp(t))', t= •-• , —1, 0, 1, 2, •-• be a real multiple stationary Gaussian process with zero mean and with covariance matrix T(h) = EIX(t)X(t-l-h)'}, where " ' " denote the transposes. We assume that the spectral density matrix f(2)=Ifik(2), j, k= 1, 2, ••• PI, —7r 2 7r, exists with f(2)= riv2F(v). Let {X(1), X(2), , X(N)} be N observables of the process X(t) and X N = (X(I-)' X(2)', ••• , X(N)')' a pN-column vector obtained by rearranging {X(1), X(2), ••• , X(N)}. We denote rN=E{XNX10.