This paper presents proofs of the strong law of large numbers and the central limit theorem for estimators of the parameters in quite general finite-parameter linear models for vector time series. The estimators are derived from a Gaussian likelihood (although Gaussianity is not assumed) and certain spectral approximations to this. An important example of finite-parameter models for multiple time series is the class of autoregressive moving-average (ARMA) models and a general treatment is given for this case. This includes a discussion of the problems associated with identification in such models.
