ESTIMATION OF THE COEFFICIENTS OF A MULTIVARIATE LINEAR FILTER USING THE INNOVATIONS ALGORITHM

Heather Mitchell and Peter Brockwell

Journal of Time Series Analysis, 1997, vol. 18, issue 2, 157-179

Abstract: 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.

Date: 1997
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