Autoregressive integrated moving average (ARIMA) models were popularized by George Box and Gwilym Jenkins in the early 1970s. Although ARIMA models were first introduced in the early 1900s and became popular in the 1960s, in 1970 Box and Jenkins developed a comprehensive approach that integrates the relevant information required to understand and use ARIMA models. They formalized their theory and methodology by developing a process to select the best ARIMA model from a group of candidate models. As a result, ARIMA models are often referred to as Box-Jenkins models. Although the theoretical notation is quite sophisticated, applying ARIMA models is not that difficult, particularly with the advances in automating the Box-Jenkins procedure using forecasting software packages.
The Box-Jenkins approach to forecasting incorporates key elements from both time series and regression methods. As a result, practitioners must have a solid understanding of regression before attempting to apply the Box-Jenkins approach to create an ARIMA model. When applying ARIMA models, two basic steps are required: (1) analysis of the data series and (2) selection of a forecasting model (from several candidate models) that best fits the data series. After plotting the time series (actual demand history), modelers use statistical tools with autocorrelation coefficients, rk, to describe the relationship between various values of the time series that are lagged k periods from one another. ...