Chapter 9: Box-Jenkins Methodology

I. Model identification:

1. Model identification examines a wide variety of possible models including autoregressive terms, moving average of past error terms, or both to capture a myriad of past data patterns in order to postulate a potential forecasting model.

2. A systematic approach is used to identify the “best” model for a given set of data.

3. The systematic approach differences the data in order to make it stationary and determining the order of the autoregressive part and/or moving average part of the model.

Model indentification begins by determining if the data is stationary by examining the ACF function of the original data. If the ACF shows positive values that trail off slowly, then the data must be differenced in order to remove the trend.

The ACF and the PACF for the resulting stationary series is used to determine the best B/J model for the series according to the following rules:

a. If the ACF trails off and the PACF shows spikes, then an AR model with order p = number of significant PACF spikes is the best model.

b. If the PACF trails off and the ACF shows spikes, the a MA model with order q= number of significant ACF spikes is the best model.

c. If both the ACF and the PACF trail off then a ARMA model is used with p=1 and q=1.

II. Model estimation and verification:

1. Once identified the “best” model is estimated such that fitted values come as close as possible to capturing the pattern exhibited by the actual data.

2. Parameters of the model are estimated and residuals are determined based upon alternative identified models. Statistical tests are available to determine the adequacy of the model.

III. Forecasting:

1. The final model is determined to be adequate (random error terms)

2. Point and confidence interval forecasts are provided for future periods.

USE OF MINITAB FOR BOX-JENKINS FORECASTING (nonstationary data)

Create data base in column 1 of spread sheet with Esc key:

MTB> ACF C1 (used to determine if data is stationary)

MTB> DIFF 1 C1 PUT IN C2 (differences data to make stationary)

MTB> PACF C2 (used with ACF to determine values of p, d, and q for best model)

MTB> ARIMA (p,d,q) C2 put in C3 and confidence limits in C4 and C5.