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I've worked with certain causal/predictive techniques when handling two time series, but this problem is different from what I am used to and I'm not sure how to proceed.

I would like to see the causal influence of a single event on multiple time series. For example, an earthquake on a particular day having an influence on future stock prices of different companies.

Is there a technique/method that allows me to address this type of question?

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Causal Events ( a.k.a as KNOWN Intervention Series ) can be incorporated into a Transfer Function which might normally include ARIMA structure and also the impact of unspecified (unknown Intervention Series .. but identifiable via Intervention Detection schemes). Software to do this , possible incorporating parameter changes and/or variance changes are not available in the "free software domain" . One can use SAS or SPSS to attempt to construct models requiring you to be an expert in this area of modelling. In terms of full disclosure this is an area that I have specializied in for many years. I suggest that you review my posts on stackexchange for more discussions on this.

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