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Could anyone show how this could be done in R? The dlm package seems to be a good start, but I can't really find any good examples to learn from.

Currently I have two timeseries of the closing prices for two stocks. I then do a rolling regression that gives me the corresponding timeseries of the beta between the two stocks.

How would I go about to implement a Kalman filter for this beta?

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Have you checked out the vingette for DLM by Petris?

Incidentally, Petris also has an R-book on the DLM package which includes estimation of beta as an example.

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