What are the pros and cons of segmented regression and regression with ARIMA errors for interrupted time-series analysis?
In what situation would I choose one method over the other? Are there any papers comparing the two techniques?
Segmented regression is flawed when you have auto-correlated data i.e. time series data. In the case of the interrupted experiment one know the point in time when the interruption occurs. Fitting local trend equations to the before and after assumes:
None of these assumptions go untested with the regression with ARIMA errors approach when conducted properly. Your answer is then use the regression with ARIMA errors approach making sure that you validate the Gaussian assumptions that were discussed here. You might want to read a well written seminal book ( unfortunately using very dated procedures ) by McCleary and Hay (1980) .
Care should be taken to ensure that the software you use has a intervention detection procedure which empirically suggests the de facto breakpoint. Intervention modelling as usually presented assumes that the user knows the true point of the intervention/interruption. Try googling "automatic intervention detection" to find out recent advances.