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Biometrika 1977 64(1):85-90; doi:10.1093/biomet/64.1.85
© 1977 by Biometrika Trust
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A comparison of estimation methods for vector linear time series models

D. F. NICHOLLS

Department of Statistics, Australian Natioanl University Canberra

Akaike (1973) showed, in the case of scalar autoregressive-moving average models, that the estimates obtained by an application of the Newton-Raphson algorithm to the approximate likelihood function are the same as those obtained by Hannan (1969). By making use of the properties of tensor products, this paper extends these ideas to show that, in the case of vector linear time series models, the estimates obtained by the application of the Newton-Raphson procedure are identical to those derived by Nicholls (1976). Consequently the estimates obtained from the Newton-Raphson algorithm, in the case of vector models, are consistent, asymptotically normal and efficient.

Key Words: Autoregressive-moving average model • Maximum likelihood • Newton-Raphson algorithm • Periodogram ordinate • Spectral density • Time series


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