Autoregressive Moving Average Models

This chapter introduces several commonly used probabilistic models for time series analysis. It briefly discusses the three kinds of models: the moving average model (MA), the autoregressive model (AR), and the autoregressive moving average model (ARMA) which are used to describe stationary time series. In addition, since certain kinds of nonstationarity can be handled by means of differencing, the chapter also studies the class of autoregressive integrated moving average models (ARIMAs). There seems to be confusion regarding the notion of stationarity and causality for AR (ARMA in general) models. The chapter clarifies this ambiguity. The usefulness of ARMA models lies in their parsimonious representation. As in the AR and MA cases, properties of ARMA models can usually be characterized by their autocorrelation functions (ACF). Since we usually process a time series before analyzing it (e.g., detrending), it is natural to consider a generalization of ARMA models, the ARIMA model. Controlled Vocabulary Terms autocorrelation function; autoregressive integrated moving average process; autoregressive model; autoregressive moving average process; moving average model