Traditional Problem Definition - Computational Intelligence in Time Series Forecasting - page 41

Model Postulation
(Heuristic)

Model Identification

Model Estimation

Model Evaluation

Model
Acceptable
?

No

Yes

Model Application

Figure 2.3. Box-Jenkins methodology of model building

The Box-Jenkins model building process assumes that the time series to be
modeled is stationary. Otherwise, it should be differenced several times until it
becomes stationary. In some cases the time series values should be manipulated so
that their mean becomes zero. Further to this, the seasonality of the time series has
to be removed, which complicates the related calculations, particularly when
building ARIMA models.

2.8.1 Model Identification

Box and Jenkins defined the model identification phase as a rough procedure for
laying down the initial model structure that matches good enough with the
collected observation data. The essence of the identification process was first
demonstrated on the example of an ARMA model, for which the required number
of parameters for both the autoregressive and the moving-average parts of the
model have been determined. This could be done using the autocorrelation
approach, usually by determining the sample autocorrelation function and the
sample partial autocorrelation function .

The sample autocorrelation function is defined as the ratio

ˆ ()

J d

ˆ ()

U d ,

ˆ (0)

J

where