Chapter 3 - ARMA Models for Stationary Time Series

Abstract

The autoregressive-moving average (ARMA) process is the basic model for analyzing a stationary time series. First, though, stationarity has to be defined formally in terms of the behavior of the autocorrelation function (ACF) through Wold's decomposition. Several simple cases of the ARMA model are then introduced and analyzed, with the partial autocorrelation function (PACF) also being defined, before the general model is introduced. ARMA model building and estimation may then be developed, and this is done via a sequence of examples designed to demonstrate some of the intricacies of selecting an appropriate model to explain the evolution of an observed time series.