I'm using the R package CausalImpact (Brodersen et. al, 2015) to estimate the impact of and event in a time series of tourists arrivals in a country. I compare it with other series of other countries used as "controls". The documentation of the package explains as assumptions:

1).-The set of control time series were themselves not affected by the intervention.

2).-Relationship between covariates and treated time series remains stable throhougt the post-period

3).-Be aware of the priors that are oart if the model.

I have read the reference paper to see that this is an implementation of a state-space model for time series using a Bayesian approach. But, my doubt is appart form the previous assumptions: There are any other assumption as stationarity of the compared series or cointegration among them to take into account before using this model?. Or we can simply use the package without worry about this usual questions crucial for other techniques as ARIMA models, etc.?

Thanks in advance and sorry for any inconvenience. José

CasualImpact is a great package for R to evaluate the dynamic impact of interventions in time series. Your data should consist of a response variable $y$ and predictors $x$, but the inference depends critically on the assumption that the predictors are covariates that were not themselves affected by the intervention. You can use nonstationary data, and in this case include nonstationary components on your model through the dynamic.regression argument of the impact function, but you need to make sure that the nonstationary structure remains unchanged across time. In Brodersen et al (2015), page 263, they warn:

It is worth emphasising that all preceding results are based on the assumption that the model structure remains intact throughout the modelling period. In other words, even though the model is built around the idea of multiple (nonstationary) components (i.e., a time-varying local trend and, potentially, time-varying regression coefficients), this structure itself remains unchanged. If the model structure does change, estimation accuracy may suffer.

This result shoud be valid either for nonstationary and cointegrated data. So if your variables have different trends or cointegration relations across time the estimation of the impact may not be valid. In case your data has a linear trend that does not change across time you can still evaluate the impact correctly. Note that you can also include time-varying local trends in the impact function, as long as the specification does not change across periods.

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