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Does anybody know a way to generalize the use of the Causal Impact google R package to multiple outcome time series?

Say I ran a time series experiment and was able to set up multiple test outcome series. To take the example in their paper: imagine I run a color change on multiple websites and want to check if color change did anything to website visits - so I have multiple outcomes. Doing an effect analysis one by one might not reveal a significant effect in each website (say the effect size is small compared to the model uncertainty). But over the 100 websites I have, I could have found a small systematic difference.

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  • $\begingroup$ If you have an experiment with a decently large sample, why do you need Causal Impact? $\endgroup$
    – dimitriy
    Commented Aug 28, 2018 at 3:43
  • $\begingroup$ Because I'm interested in the Bayesian framework and in the synthetic control approach to timeseries. They are not randomised controlled experiments. $\endgroup$
    – f.g.
    Commented Aug 29, 2018 at 19:30
  • $\begingroup$ In that case, it might make sense to edit your post and alter "I ran an experiment" to whatever you think would be a correct description. $\endgroup$
    – dimitriy
    Commented Aug 29, 2018 at 21:03

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Causal impact relies on two ideas: (i) Kalman Filters and (ii) Bayesian Variable selection. Both of these ideas can easily be extended to multidimensional settings. Koopman and Durbin (2012) is the foremost textbook on Kalman Filters.

To answer your question, Causal Impact does not allow for multiple outputs. It's possible but would require someone re-deriving the underlying distributions of Causal Impact for a multivariate case. If you have some free time in a PhD, go for it! Otherwise, have you considered looking at frequentist approaches like gsynth by Xu (2017)?

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  • $\begingroup$ I think adding some links or at least complete references would improve this answer. $\endgroup$
    – dimitriy
    Commented May 26, 2020 at 17:28

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