Maximum likelihood estimation of regression models with autoregressive-moving average disturbances

TLDR

The regression model with autoregressive‑moving average disturbances can be reformulated for Kalman filtering. Using Kalman filtering, the generalized least squares estimator can be computed without inverting the disturbance covariance matrix, allows efficient forecasting of future dependent values, and provides a basis for exact maximum likelihood estimation. Residuals from the Kalman filter appear useful for diagnostic checking, and the method offers computational and theoretical advantages over alternatives.

Abstract

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.