I am familiar with using regression with ARIMA errors to model interrupted time-series, in order to estimate the change in magnitude caused by a policy intervention. These models seem to be designed for a single time series, and thus if multiple time-series are analysed a model must be fit separately for each time-series.
I am interested in analysing the national impact of a policy intervention, the implementation of which was staggered in time across all (eight Australian) states. I can see three possible analysis approaches here:
- Fit a separate ARIMA model for each state
- Attempt to fit an aggregate national model, perhaps with one dummy variable indicating partial implementation and another indicating complete implementation
- Find a different model that works explictly on panel data. This would hopefully bring some kind of compromise between the no-pooling approach 1 and the complete pooling approach 2.
What sort of approach would you recommend here?