Practical Data Analysis with JMP®

Autoregressive Models

When we use regression analysis to model the trend of a time series, the dependent variable is the observed data Y_i and the independent variable is just the time period, t. An alternative approach is to model Y_i as a function of one or more prior observations of Y. As with exponential smoothing, there are many variations on this basic idea of an autoregressive model. In this section, we'll examine one such model from the general class of AutoRegressive Integrated Moving Average, or ARIMA models. These are also sometimes called Box-Jenkins models, after the two statisticians George Box and Gwilym Jenkins who developed the techniques in the 1960s and early 1970s.

The ARIMA analysis properly is performed on a stationary (without ...