Applied Time Series Analysis for the Social Sciences

6ARIMA Intervention Models

Chapter 1 showcases the difficulty behind deciding if the 2007 US troop surge in Iraq led to a decrease in US troop fatalities. While the surge was followed by a sharp drop in the number of deaths, it is unclear whether the drop was associated with the surge or merely part of the normal fluctuation in the series. This is an example of a problem that may be addressed in an ARIMA context if necessary assumptions are met: we can model the baseline variation as an ARIMA process and then test whether there is a deviation from the baseline that is associated with the intervention. This is the strategy underpinning “ARIMA impact assessment” associated with a class of models generally referred to as “ARIMA intervention models.” Modeling the impacts of interventions this way is especially useful when we either do not know or cannot measure key drivers of the baseline variation.

These models are based on three critical assumptions. First, we must know when the event occurs and have sufficient information to model it. Typically, the event or intervention will be modeled as an off/on (0/1) indicator variable; the timing must be known in advance. Second, the intervention is assumed to affect the dependent variable, but the dependent variable must not affect the intervention. Vector autoregression (VAR) models, covered in Chapter 12, are able to address situations in which this assumption cannot be met. (Indeed, since ARIMA models can be written as special cases ...