Models with Regressor Variables

Up to this point in the book, we have considered models based upon a single series. However, in many applications, additional information may be available in the form of input or regressor variables; the name may be rather opaque, but we prefer it to the commonly-used but potentially misleading description of independent variables. We then refer to the series of interest as the dependent series. Regressor series may represent either explanatory or intervention variables.

An explanatory variable is one that provides the forecaster with additional information. For example, futures prices for petroleum products can foreshadow changes for consumers in prices at the pump. Despite the term “explanatory” we do not require a causal relationship between the input and dependent variables, but rather a series that is available in timely fashion to improve the forecasting process. Thus, stock prices or surveys of consumer sentiment are explanatory in this sense, even though they may not have causal underpinnings in their relationship with a dependent variable.

An intervention is often represented by an indicator variable taking values 0 and 1, although more general forms are possible. These variables may represent planned changes (e.g., the introduction of new legislation) or unusual events that are recognized only in retrospect (e.g., extreme weather conditions). Indicator variables may also be used to flag unusual observations or outliers; if such values are not identified they can distort the estimates of other parameters in the model.