Applied Time Series Analysis for the Social Sciences

7ARIMA with Continuous Explanatory Variables

In Chapter 6, we introduced simple interventions into our ARIMA models. We saw that as long as we could assume that the ARIMA (stochastic) portion of the series we were modeling was unaffected by the intervention, we could use the ARIMA model as a baseline against which to evaluate the intervention's impact. In practical terms, this means we are assuming that the intervention affects neither the omitted independent variables that we relegated by construction to the ARIMA piece nor the structure of any random autocorrelation. This affords us the remarkable capability of providing some control for the omitted variables even when we do not know what they are and/or cannot measure them. It is a partial explanation behind the finding cited in Chapter 1 that shook the time series community: atheoretical ARIMA models were providing more accurate forecasts than multiple equation models that carefully took theory into consideration.

Our atheoretical ARIMA models are at best, though, an approximation for the variation of the omitted variables, and the approximation is based on the assumption that the omitted variables can be represented by the same model over time. Explicitly modeling the variables we are able to model is always preferred. This chapter introduces the methodology for doing so when our explanatory variable is continuous, and the extra steps that must be taken to model the dynamic relationship and minimize any spurious effects. ...