I will describe my question with the following example.

Imagine I have 3 series that are cointegrated and there is another that is a policy variable. This policy variable is I(0) and was ranging around a certain level and after was dramatically reduced to another level and stayed in that level until the end of the series. When including this policy variable as exogenouns variable outside the cointegration space, can I apply interrputed time series analysis to see the short term effect of the effect of the policy? I think yes, but I am not sure.

Second case, Imagine that the policy variable is I(1) and totally exogenous because it does not depend at all (or almost at all to be more precise and not to exagerate), Can I include it in the conintegration space as exogenouns and apply also interrupted time series analysis? In this case, I think no, but I am not sure.

Finally, I have 58 observations of yearly data. I know that it's not a big sample. Then, is it "acceptable" to model a cointegration system with 3 variables and a trend in the cointegration space and two exogenous outside with 1 or 2 lags? Here I guess it's too much for 55 or 65 observations


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