ARIMA Models

Abstract

Classical regression is often insufficient for explaining all of the interesting dynamics of a time series. For example, the ACF of the residuals of the simple linear regression fit to the price of chicken data (see Example 2.4) reveals additional structure in the data that regression did not capture. Instead, the introduction of correlation that may be generated through lagged linear relations leads to proposing the autoregressive (AR) and autoregressive moving average (ARMA) models that were presented in Whittle [209]. Adding nonstationary models to the mix leads to the autoregressive integrated moving average (ARIMA) model popularized in the landmark work by Box and Jenkins [30]. The Box–Jenkins method for identifying ARIMA models is given in this chapter along with techniques for parameter estimation and forecasting for these models. A partial theoretical justification of the use of ARMA models is discussed in Sect. B.4.