Chapter 8 - Autoregressive Moving Average Models

Abstract

Autoregressive moving average (ARMA) models play a key role in the modeling of time series. The linear structure of ARMA processes also lead to a substantial simplification of linear prediction. An ARMA process consists of two models: an autoregressive (AR) model and a moving average (MA) model. Compared with the pure AR and MA models, ARMA models provide the most effective linear model of stationary time series since they are capable of modeling the unknown process with the minimum number of parameters. In this chapter, for ARMA models, we study covariance structure, parameter estimation, asymptotic normality, and power spectral density, and introduce Yule-Walker equations and the Durbin-Levinson prediction algorithm. In addition, we also introduce autoregressive integrated moving average (ARIMA) models and multivariate ARMA.