Some recent advances in time series modeling

Abstract

The aim of this paper is to describe some of the important concepts and techniques which seem to help provide a solution of the stationary time series problem (prediction and model identification). Section I reviews models. Section II 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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g_{\infty}</tex> is developed, and the time series modeling problem is defined to be the estimation of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g_{\infty}</tex> . Section III reviews estimation theory. Section IV describes autoregressive estimators of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g_{\infty}</tex> . It introduces a criterion for selecting the Order of an autoregressive 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.