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I have time series data for a set of cities that goes back for about 10 years. I also have the data at the state level for almost 30 years. There was an event that occurred about 20 years ago, that is captured in the longer, state level data, but not the city data, that I would like to investigate at the city level.

What I think might be useful is to create some kind of ARIMA model that regresses the state data as an exogenous variable. If I were to do this, how do I use the model to backfill the city data such that it ends at the same point as where the actual city data starts? Is there already a canonical method of doing something like this? Thanks for any help you can give (literature references, R libraries, etc.)

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To do your backcasting, you could use the state level data as a causal variable. You would constrain the variable into the model.

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  • $\begingroup$ It's that last part that I'm unsure about. How do I constrain my y_t such that it ends at the right place? I'm sure this is backcasting 101, but I guess that's what I'm asking - where can I find a backcasting 101 formula with external regressor? Thanks. $\endgroup$ – njnnja Mar 19 '13 at 19:28

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