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I have multiple time series where at any point in the time series, an event can occur that I believe has an effect on the time series. This event can happen at different times for each of the different time series. How would I go about estimating the effect of this event on a time series where the event has not yet occurred? Ideally this would be some function of the time series itself. Thanks!

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One approach would be to gauge the difference between the "normal" variations of the time series and the observed quantities at and/or after the event. This approach in three steps (1) MODEL: Build a model for the time series, ideally only using the data before the event, and ideally yet, with a good amount of data so as to make the model robust. (2) INFER: Infer a "prediction" of what the time series "should" look like at/after the event (3) COMPARE: The difference between the prediction and the actual can be taken to be the effect of the event.

You could take standard ARIMA models to for the MODEL part. I would suggest gravitating towards Bayesian models for this purpose.

You can find some more details of (an instance of) this approach here:

http://www.r-bloggers.com/causalimpact-a-new-open-source-package-for-estimating-causal-effects-in-time-series/

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