Solutions to the stationary time series modeling and prediction problem

The aim of this paper is to describe some of the important concepts and techniques which seem to me to help provide a solution of the stationary time series problem (prediction and model identification). Section 1 reviews models. Section 2 reviews prediction theory and develops criteria of closeness of a "fitted" model to a "true" model. The central role of the infinite autoregressive transfer function g∞ is developed, and the time series modeling problem is defined to be the estimation of g∞. Section 3 describe auto-regressive estimators of g∞. It introduces a criterion for selecting the order of an auto-regressive estimator which can be regarded as determining the order of an AR scheme when in fact the time series is generated by an AR scheme of finite order.