TECHNIQUE #8: Box Jenkins Models
Due to its complexity, only a most general idea of Box-Jenkins procedures (manytimes referred to as ARIMA models) can be offered here. You can obtain more detailed examples and information in the references.
BASIC IDEA: In contrast to other techniques, Box-Jenkins is a procedure which uses a variable's past behavior to select the best forecasting model from a general class of models. It assumes that any time series pattern can be represented by one of three categories of models. These categories include:
Autoregressive models: forecasts of a variable based on linear function of its past values
Moving Average models: forecasts based on linear combination of past errors
Autoregressive-Moving Average models: combination of the previous two categories
Note that one of the key questions is how many past values (the focal variable and/or its errors) should be included in the model.
PROCEDURE: Generally speaking, there are essentially three stages to a Box-Jenkins procedure:
1. Identifying the tentative model. Which of the three categories listed above is identified as the appropriate category is determined by first making the data stationary (usually by differencing the data) and then analyzing the autocorrelations and partial autocorrelations of the stationary data. Note that there are theoretical autocorrelation and partial autocorrelation profiles for each of the possible models. Therefore, determining the appropriate type of model for a specific situation is mainly a matter of matching the observed correlations to the theoretical correlations.
2. Determining the parameters of the model. This is similar to estimating the parameters in regression analysis.
3. Application of the model.
COMMENTS: Box-Jenkins approaches to forecasting provide some of the most accurate short-term forecasts. However, it requires a very large amount of data.