A method is proposed for the estimation of a general class of scalar linear time series models. The model takes the form of a stochastic difference equation for the dependent variable with exogenous variable inputs, and the disturbances are autocorrelated through an autoregressive moving average process. In the present paper an asymptotically efficient yet computationally simple estimation procedure (in the time domain) is derived for this model. The resulting estimator is shown to be asymptotically equivalent to the maximum likelihood estimator and to possess a limiting multivariate normal distribution.