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I have many time series and a set of dates (key events eg public holidays or big sales days). There are too many for me to look as manually and determine if either an increase or decrease occured as a result of the event. Is there some algorithm that I could use? I am currently using R.

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The keyword for you is Intervention Analysis. You might find many resources over the Web, personally I liked Prof. Ruey Tsay's notes. As for brief overview - you'll add extra variables to the series, which indicate whether a particular event takes place, and test their influence on the series.

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To answer the question whether or not a KNOWN event has had a statistically significant effect you can use the T ration for the event if the model errors are free of auto-regressive structure and the model errors do not contain any deterministic structure such as level shifts/local time trends/seasonal pulses/pulses. Furthermore the variance of the model's errors must be invariant over time and independent of the level of Y. Finally your model parameters must be invariant over time. Finally all of the significant lag structures in the known X's must be in the model. If all of these requirements are in place then you are free to interpret the T value in the standard way otherwise the T values are relatively meaningless. If these requirements are not "provable" then you might want to look at some commercially available software as the offerings via R are not very good.

The pioneering work of Tsay was the identification of UNKNOWN events.

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