Transfer Functions in Custom ARIMA Models

The Transfer Function tab (only present if independent variables are specified) allows you to define transfer functions for any or all of the independent variables specified on the Variables tab. Transfer functions allow you to specify the manner in which past values of independent (predictor) variables are used to forecast future values of the dependent series.

Transfer Function Orders. Enter values for the various components of the transfer function into the corresponding cells of the Structure grid. All values must be non-negative integers. For numerator and denominator components, the value represents the maximum order. All positive lower orders will be included in the model. In addition, order 0 is always included for numerator components. For example, if you specify 2 for numerator, the model includes orders 2, 1, and 0. If you specify 3 for denominator, the model includes orders 3, 2, and 1. Cells in the Seasonal column are only enabled if a periodicity has been defined for the active dataset (see "Current Periodicity" below).

  • Numerator. The numerator order of the transfer function. Specifies which previous values from the selected independent (predictor) series are used to predict current values of the dependent series. For example, a numerator order of 1 specifies that the value of an independent series one time period in the past--as well as the current value of the independent series--is used to predict the current value of each dependent series.
  • Denominator. The denominator order of the transfer function. Specifies how deviations from the series mean, for previous values of the selected independent (predictor) series, are used to predict current values of the dependent series. For example, a denominator order of 1 specifies that deviations from the mean value of an independent series one time period in the past be considered when predicting the current value of each dependent series.
  • Difference. Specifies the order of differencing applied to the selected independent (predictor) series before estimating models. Differencing is necessary when trends are present and is used to remove their effect.

Seasonal Orders. Seasonal numerator, denominator, and differencing components play the same roles as their nonseasonal counterparts. For seasonal orders, however, current series values are affected by previous series values separated by one or more seasonal periods. For example, for monthly data (seasonal period of 12), a seasonal order of 1 means that the current series value is affected by the series value 12 periods prior to the current one. A seasonal order of 1, for monthly data, is then the same as specifying a nonseasonal order of 12.

Current Periodicity. Indicates the periodicity (if any) currently defined for the active dataset. The current periodicity is given as an integer--for example, 12 for annual periodicity, with each case representing a month. The value None is displayed if no periodicity has been set. Seasonal models require a periodicity. You can set the periodicity from the Define Dates dialog box.

Delay. Setting a delay causes the independent variable's influence to be delayed by the number of intervals specified. For example, if the delay is set to 5, the value of the independent variable at time t doesn't affect forecasts until five periods have elapsed (t + 5).

Transformation. Specification of a transfer function, for a set of independent variables, also includes an optional transformation to be performed on those variables.

  • None. No transformation is performed.
  • Square root. Square root transformation.
  • Natural log. Natural log transformation.

To Define Transfer Functions

This feature requires the Forecasting option.

  1. From the menus choose:

    Analyze > Forecasting > Create Models...

  2. On the Variables tab, select ARIMA for Method.
  3. Click Criteria....
  4. Click the Transfer Function tab.
  5. Select one or more independent variables and define the transfer function for the selected variable(s).
  6. Optionally, select another set of variables and define a different transfer function for that set, and repeat for as many different transfer functions as are needed.
  • You can update the transfer function for any set of variables by selecting that set of variables and entering the changes.
  • Any existing transfer function for a variable is displayed when that variable is selected.