Box-Jenkins (ARIMA) Models Wizard

The Box-Jenkins(ARIMA Models) Wizard on the Time Series Menu provides a convenient interface to the BOXJENK instruction for estimating ARIMA models. Selecting the Wizard brings up the following dialog box:

The fields on the header are:

Series

Use this field to select the dependent variable for the ARIMA model. This usually starts out empty so that you have to select a series from the popup menu.

Sample Start and End

Use these fields if you want to specify the start and/or end of the sample range. Leave these blank if you want to use the default range.

Residuals to

You can use this field to store the estimated residuals to a series.

Define Equation

This field allows you to save the estimated EQUATION. Just type in a new name for the equation.

Differences Tab

None/One Regular/etc.

Use these radio buttons to select which, if any, regular and/or seasonal differencing you want to include in a model. If you need help choosing this, try the @BJDIFF procedure.

No Constant/Zero Mean, Estimated Constant, Remove Mean

Use these radio buttons to include an estimated constant term in the model, to remove the mean from the dependent variable before estimating the model, or to omit any constant term. Note that this choice interacts with the differencing. A trending series can either be represented by one difference plus a non-zero constant, or two differences (in any combination) with no constant.

ARMA Parameters Tab

The ARMA Parameters Tab has the following look:

Use these fields to select the AR, MA, and Seasonal AR and MA lags you want to include in the model. For each category, you can use the field on the left hand side to select consecutive lags from 1 to L, where L is the value input. Or, use the field on the right to list the specific lags you want to include, separated by a space or a comma. The example above requests 2 AR and 2 MA. An example with skipped lags is below, which has MA's on 1, 6, 7 and 9 only.

The Clear Settings button will reset all fields to have no lags on any polynomial.

Other Inputs Tab

The Other Inputs tab is for any other regression or shift effects other than the ARMA parameters and constants. Note that any such variables have to be created earlier. These come in two forms: the Transfer/Intervention Form is the original method from the Box-Jenkins literature which adds terms which have a structure similar to the ARMA model itself—lags and dynamics are handled through the numerator, denominator and delay parameters. The Regression Form creates a mean model which takes the standard form for a linear regression with any lags and dynamics handled by including specific lags in the list of regressors. An example with the Other Inputs tab exposed (with the Regression Form button selected) is

Regression Form

You can either type in a list of explanatory variables in Regression Format, separating variables with at least one blank space, or click on the series list button to select from a list of the series available in memory with a Select Regressors dialog box.

GLS Options

Turns on the GLS option on the BOXJENK, which reorders the output, and has the same effect as turning on both the MAXL and APPLYDIFFERENCES options.

Transfer/Intervention Form

Selecting the Transfer/Intervention Form radio button changes the form of the tab to something like

Click on the <<Add<< button if you want to add transfer function or intervention model terms. This will bring up the following dialog box:

Use the dialog to select a transfer or intervention series and the desired order of numerator and/or denominator lags and the number of delay lags that you want to apply to this term. Click OK to add the resulting term to your model, which will drop back to the main Wizard dialog. Each transfer item that you've added will show as one line in the scrolling box on the tab.

You can then click on <<Add<< again if you want to add an additional Transfer/Intervention term or >>Remove>> to remove any unwanted ones.

Apply Differences to These

Turn this check-box on if you want to apply any differencing selected in the Differencing field to the Transfer/Intervention or Regression terms (see the APPLYDIFF option in BOXJENK for more details).

Estimation Tab

Conditional Least Squares/Maximum Likelihood

This chooses the objective function used in estimation. Maximum likelihood is more complicated, but should produce the same answers on all software which uses it, while conditional least squares is simpler, generally less likely to create non-linear estimation problems, but depends upon the handling of pre-sample information, which can be different among different software packages.