An Introduction to ARMA Models

Abstract

The focus of this chapter is on autoregressive moving average (ARMA) models, which were introduced in a simple form in Chapter 1. These models are not only of interest in their own right, they serve to provide a background to interpret many of the issues arising in the context of unit roots and integrated time series. The ‘ARMA’ notation indicates that there are two components to the structure of these models. The first part is the autoregressive (AR) component and the second the moving average (MA) component. The ARMA model is said to be integrated if a unit root, or roots, can be extracted from the AR component, in which case the appropriate notation is ARIMA, for an autoregressive, integrated moving average model. The kind of structure of interest in this chapter is where one of the roots of the AR polynomial might be a unit root whilst the others are outside the unit circle. The case of two unit roots is considered in Chapter 11 and the roots of a polynomial are considered extensively in Appendix 2.