The identification of ARMA models

Abstract

SUMMARY We present a new powerful method for determining the order of ARMA (p, q) models having small sets of observations. The procedure is based on an autoregressive order determination criterion and on linear estimation methods. Simulated data are used to demonstrate the capabilities of the approach. for a survey. Nevertheless the reliability and adaptability of the methods remain at best tenuous. In this paper we propose a simple but accurate procedure based on an autoregressive order determination criterion and linear estimation methods to identify the order of ARMA processes from a finite set of observations. The paper is organized as follows: in ? 2 we describe our approach; in ? 3 we demonstrate the performance of our identification procedure based on simulations of several model structures with varying number of observations; and ? 4 contains concluding remarks. It is important that in reality the order of any process based on finite samples may never be correctly identified by any procedure. All models are simplifications of reality. Their value and strength lie in their ability to explain the current situation and to predict the future. Our procedure, therefore, should be viewed as one which parsimoniously identifies the order of the ARMA model which reasonably depicts the underlying process governing the behaviour of the available data (Box & Jenkins, 1976, Ch. 1). For brevity we assume that the reader is familiar with the characteristics and properties of ARMA models. Unless otherwise stated we use the notation and conventions of Box