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I am looking for a good introduction into or an overview about interrupted time series or intervention analyses for time series. Perhaps also considering change point detection or event study analyses.

This questions deals with literature regarding R implementations but I am looking for a more general treatment (including theoretical considerations). I furthermore could not find the topic discussed in the literature outlined in that question (Rob Hyndman, for example, discuss interventions only very briefly in a subchapter and I couldn't find it in Shumway and Stoffer). Here is an interesting answer outlining one specific approach how to deal with that topic.

Furthermore, is there a widely understood terminology for this kind of analyses? It seems for me that each field gives these statistical approaches different names.

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In general , the topic is Intervention Modelling . If you don't precisely know the date and the type of intervention this is referred to as Intervention Detection where a carefully launched search process is implemented to identify the date and type of intervention. Some limited implementations of this require " THE FORM OF THE ARIMA MODEL" to be pre-specified , others are much more general insofar as they simultaneously determine the arima model and the date and type.

An example of having to pre-specify the arima model form (with possible unintended consequences) is here https://www.r-bloggers.com/outliers-detection-and-intervention-analysis.

A seminal article is here http://docplayer.net/12080848-Outliers-level-shifts-and-variance-changes-in-time-series.html leading to https://autobox.com/pdfs/ARIMA%20FLOW%20CHART.pdf and https://autobox.com/pdfs/SARMAX.pdf . Early work assumed the date and form of the intervention which of course may be productive or counter-productive based upon the actual data.

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