Statistical forecasting for stochastic processes

The main purpose of this paper is to review the efficiency properties of least-squares predictors when the parameters are estimated. It is shown that the criterion of asymptotic best unbiased predictors for general stochastic models is a natural analogue of the minimum mean-square error criterion used traditionally in linear prediction for linear models. The results are applied to log-linear models and autoregressive processes. Both stationary and non-stationary processes are considered.This paper is based on a key note lecture given at the meeting of The Institute of Management Sciences and the Operations Research Society of America, held in Williamsburg, Virginia, January 7–9, 1985.