I am currently doing a project that employs intervention analysis. I understand that we are supposed to use the pre-intervention data to formulate a noise model. However, Walter Enders said in his textbook ( Applied Econometric Time Series - 2nd Edition, page 244) that we are to use the longest data span (i.e either pre or post interventions) to find a plausible set of ARIMA models. He also quoted Enders et al (1990) "Assessing the impact of terrorist‐thwarting policies: An intervention time series approach" which actually used the post-intervention model to come up with a plausible model.
I would actually prefer to stick to using pre-intervention data to form my noise model. However, my pre-intervention data consists of only 38 months. On the other hand, i have 94 months for post intervention data. The noise model that i created based on Box-Jenkins 3 step procedure (in this case using the 38 months - pre intervention) is not satisfactory. Therefore, I would to ask for opinions whether I should go ahead and follow Enders recommendation (i.e use post intervention).
I have actually done it in R. Both methods came up with the same ARIMA model. However, the model diagnostics for the residual pre-intervention series did not satisfy the requirements. On the other hand, the residual for post-intervention satisfied the requirements (ie. are white noise).
It will be good if you can explain why both methods (using pre or post intervention to formulate a noise model) is interchangeable. And what are the assumptions needed (if any)? I will also greatly appreciate if you can recommend published papers that actually make use of post-intervention data for the noise model so that I know Enders is not the only one recommending this approach.