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I have a multivariate time series dataset, from which I am building an ITS (Interrupted Time Series) model by using facebook's Prophet to construct the counterfactual. Let's say I have a y variable that's affected by x1,x2,...xn. How do I quantify the treatment effect, that is the difference between the counterfactual and the post-interruption slope ?

I read a couple of papers and posts stating that we needed to evaluate:

  • change in level
  • change in level at later time point (to check for lag effect)
  • the slope of the post-interruption

I am confused about this later part, measuring the post-interruption slope:

  • should I simply take the data as represented by the graph below, with y as outcome and x as time, and compare the marginal effect of time on outcome (in a linear, univariate form) between the counterfactual and post-interruption data ?
  • would it make sense here to run 2 OLS (one with pre-interruption + counterfactual data, the other with pre-interruption + post interruption) to compare the importances of the independent variables between the counterfactual and the actual data ?

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I apologize if those two questions are basic or seem overly simplistic, I am completely new to ITS. Thanks in advance !

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