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Using Predictor Variables |

The `Dynamic Regressor` option allows you to specify a complex time series
model of the way that a predictor variable influences the series that you are
forecasting.

When you specify a predictor variable as a simple regressor, only the current period value of the predictor effects the forecast for the period. By specifying the predictor with the Dynamic Regression option, you can use past values of the predictor series, and you can model effects that take place gradually.

Dynamic regression models are an advanced feature that you are unlikely to find useful unless you have studied the theory of statistical time series analysis. You may wish to skip this section if you are not trained in time series modeling.

The term *dynamic regression* was introduced by Pankratz (1991)
and refers to what Box and Jenkins (1976) named *transfer function models*.
In dynamic regression, you have a time series model, similar to an ARIMA model,
that predicts how changes in the predictor series affect the dependent
series over time.

The dynamic regression model relates the predictor variable to the expected value of the dependent series in the same way that an ARIMA model relates the fluctuations of the dependent series about its conditional mean to the random error term (which is also called the innovation series). Refer to Pankratz (1991) "Forecasting with Dynamic Regression Models," and Box and Jenkins (1976) "Time Series Analysis: Forecasting and Control" for more information on dynamic regression or transfer function models. See also Chapter 7, "The ARIMA Procedure,".

From the Develop Models window,
select `Fit ARIMA Model.`
From the ARIMA Model Specification window,
select `Add` and then select `Linear Trend`
from the menu (shown in Display 27.1).

Now select `Add` and select `Dynamic Regressor`.
This displays the `Dynamic Regressors Selection` window,
as shown in Display 27.11.

You can select only one predictor series when specifying
a dynamic regression model.
For this example, select VEHICLES, "Sales: Motor Vehicles and Parts."
Then select the `OK` button.

This displays the `Dynamic Regression Specification` window,
as shown in Display 27.12.

This window consists of four parts.
The `Input Transformations` field allows you to transform or lag
the predictor variable.
For example, you might use the lagged logarithm of the variable
as the predictor series.

The `Order of Differencing` field allows you to specify simple and seasonal
differencing of the predictor series.
For example, you might use changes in the predictor variable
instead of the variable itself as the predictor series.

The `Numerator Factors` and `Denominator Factors` fields
allow you to specify the orders of simple and seasonal numerator
and denominator factors of the transfer function.

Simple regression is a special case of dynamic regression in which the
dynamic regression model consists of only a single regression coefficient
for the current value of the predictor series.
If you select the `OK` button without specifying any options
in the Dynamic Regression Specification window,
a simple regressor will be added to the model.

For this example, use the `Simple Order` combo box for
`Denominator Factors` and set its value to 1.
The window now appears as shown in Display 27.13.

This model is equivalent to regression on an exponentially weighted infinite distributed lag of VEHICLES (in the same way an MA(1) model is equivalent to single exponential smoothing).

Select the `OK` button to add the dynamic regressor to the
model predictors list.

In the ARIMA Model Specification window, the Predictors list should now contain two items, a linear trend and a dynamic regressor for VEHICLES, as shown in Display 27.14.

This model is a multiple regression of PETROL on a time trend variable
and an infinite distributed lag of VEHICLES.
Select the `OK` button to fit the model.

As with simple regressors, if VEHICLES does not already have a forecasting model, an automatic model selection process is performed to find a forecasting model for VEHICLES before the dynamic regression model for PETROL is fit.

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