The efficient estimation of vector linear time series models

SUMMARY A procedure is given to estimate efficiently the coefficients of a general class of vector linear time series models. The procedure is based on spectral techniques. The estimated model is shown to contain, as particular cases, many of the time series models which have appeared in the literature. The efficient estimation of the coefficients of scalar autoregressive-moving average models has been considered by Hannan ( 1969) and generalized to the case where exogenous variables have been included by Hannan & Nicholls (1972). In his 1969 paper Hannan considered the extension of the procedure to the vector case only for the moving average model. The purpose of the present paper is to extend the earlier work to the estimation of vector auto- regressive-moving average models with exogenous variables. Indeed using a similar pro- cedure to that of Hannan & Nicholls (1972), we develop a procedure for the efficient esti- mation of the coefficients of models of the form q p