The Role of Linear Recursive Estimators in Time Series Forecasting

This paper presents a descriptive synthesis of a number of a linear recursive estimator (LRE) procedures for time series forecasting, i.e., procedures which involve parameter updates proportional to the last period forecast error. It is stressed that both constant and variable parameter procedures exist among LRE's. General requirements for stability of parameter estimates are given, as are general forms for parameter estimate covariance matrices that appear in forecast variance determinations. Procedures explicitly considered are the Kalman filter, dynamic autoregression, the Carbone-Longini adaptive estimation procedure, generalized least squares, Widrow's least mean square, and the Makridakis-Wheelwright generalized adaptive filtering.