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Q1: Is there any Arima (p,d,q) model that can forecast interventions (pulse) itself? I know that I can use xreg or even xtransf arguments as the covariates to include the intervention over the observed time series.

The problem is that I don’t know the new values of the covariates to include in the predict function to do the forecasts.

Q2: Can we simulate (estimate) these new covariates? If yes, how? I think that depends on the probability of having pulse. But how we can estimate these probabilities?

To be more precise, I want to develop a time series model that can capture the interventions and also be able to forecast them! Is that even possible? Maybe I am asking too much :) I appreciate any comment, suggestion or reference.

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It is a little puzzling to hear you talk about forecasting interventions. By definition intervantions are planned and time with the intention of causing change in the process. Usually the time of the intervention is known and the magnitude of the effect (such as a level shift) is the main interest. Sometimes it is known that a intervention occurred but the exact time of occurrence is not known and the data can be used to try to determine the time of the intervention as well. – Michael Chernick Aug 7 '12 at 17:19
If you are thinking of a periodic occurrence of events that create level shifts then perhaps it is possible to forecast them if they have occurred a few times at regular intervals. – Michael Chernick Aug 7 '12 at 17:21
Thanks for the reply. The interventions are indeed planned over the observation period of time series responses, but not over the forecast period. The intervention that I am working with is exteremly rare, so it must be difficult to forecast them. – Stat Aug 7 '12 at 17:58
But I am sure there must be some models to do so. The time of occurrence of this rare event over the forecast period is important for me, since the magnitude of the effect can be captured by the Arima model. – Stat Aug 7 '12 at 18:07
If there is a systematic history of interventions then there should be a way to forecast their occurrence. I believe there has been discussion on this website about something called mosaics which i believe are patterns that can be predicted and your interventions would fall into this category. – Michael Chernick Aug 7 '12 at 18:19
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In response to your second question. I had found this paper a few months ago which is trying to exactly what you are proposing.

http://www.upo.es/eps/troncoso/papers/PRL2011.pdf

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Hey Tom, thanks a lot for the paper. Yes this is exactly what I was looking for :) – Stat Aug 10 '12 at 6:37
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In doing a keyword search for mosaic on this site I have so far only found mosaic plots usually in the context of categorical data analysis. But I distinctly recall somthing on time series.

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