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Estimation Of The Coefficients Of A Multivariate Linear Filter Using The Innovations Algorithm

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  • Heather Mitchell
  • Peter Brockwell

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.

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  • Heather Mitchell & Peter Brockwell, 1997. "Estimation Of The Coefficients Of A Multivariate Linear Filter Using The Innovations Algorithm," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(2), pages 157-179, March.
    • Handle: RePEc:bla:jtsera:v:18:y:1997:i:2:p:157-179
    DOI: 10.1111/1467-9892.00044
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    Cited by:

    1. Jonas Krampe & Timothy L. McMurry, 2021. "Estimating wold matrices and vector moving average processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(2), pages 201-221, March.

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