Learning Dynamic Beta Estimation with Kalman Filtering

Summary

The document asks how to replace a rolling regression with a Kalman filter to estimate a time-varying beta between two stocks. It identifies R’s dlm package as a possible tool, but does not provide an implementation, specify a state-space model, or explain how to estimate the filter’s parameters. The accepted response points readers to the package vignette and a book by its author, noting that the book includes beta estimation as an example.

The practical lesson is that a dynamic beta can be approached through a dynamic linear model, with the package documentation and worked example serving as the learning path. The document offers no empirical comparison with rolling regression and gives no evidence about trading performance. It also leaves important modeling choices open, such as whether the beta follows a random walk and how observation noise is set. Readers will need the referenced materials to turn the suggestion into a working estimate.

Key ideas

• A Kalman filter can be used to estimate a beta that changes over time between two stocks.
• The question concerns implementing this approach in R with the dlm package.
• The response recommends the package vignette and its author’s book as learning resources.
• The document provides no model specification, code, or performance evidence.

Tags

# How does Kalman filtering of beta in pairs trading model work in R?


# How does Kalman filtering of beta in pairs trading model work in R?












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?

## Answer by Ram Ahluwalia (score 5, accepted)

https://quant.stackexchange.com/a/2352

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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