© 1979 by Biometrika Trust
Maximum likelihood estimation of regression models with autoregressive-moving average disturbances
Department of Statistics, London School of Economics
Faculty of Social Sciences, University of Kent Canterbury
The regression model with autoregressive-moving average disturbances may be cast in a form suitable for the application of Kalman filtering techniques. This enables the generalized least squares estimator to be calculated without evaluating and inverting the covariance matrix of the disturbances. The problem of forecasting future values of the dependent variable is also effectively solved when the Kalman filter technique is applied. Furthermore, the properties of the residuals produced by the filter suggest that they may be useful for diagnostic checking of the model. The Kalman filter algorithm also forms the basis of a method for the exact maximum likelihood estimation of the model. This may well have computational, as well as theoretical, advantages over other methods.
Key Words: Autoregressive-moving average process • Diagnostic checking • Forecasting • Generalized least squares • Gram-Schmidt orthogonalization • Kalman filter • Maximum likelihood • Prediction error • Recursive residual • Regression