ESTIMATION OF THE COEFFICIENTS OF A MULTIVARIATE LINEAR FILTER USING THE INNOVATIONS ALGORITHM
Heather Eunice Mitchell, Peter J. Brockwell · Journal of Time Series Analysis · 1997
It is shown under mild conditions that the estimators of the coefficient matrices obtained by applying the innovations algorithm to the sample covariances of observations of the multivariate linear time series Xt = ∑∞j=0ψiZt, t = 0, ±1, ±2, . . ., are consistent. The asymptotic distribution of the estimators is found to have a very simple form which generalizes the corresponding univariate result of Brockwell and Davis (Simple consistent estimation of the coefficients of a linear filter. In Stochastic Processes and Their Applications. Amsterdam: North‐ Holland, pp. 47‐‐59). The asymptotic distribution of the corresponding estimator of the spectral density matrix is also derived. Some simulation results are presented to illustrate the small‐sample behaviour of the estimators.