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There is a dilemma between choosing short history (1-2 years) and long history (5-10 years) for a regression model. Are there any resources that offer some findings on pros and cons of these two? From the perspective of a long term asset/fund manager, which one would make more sense?

Clearly, the short model would depict the most recent relationship. However, the long model would capture stress periods, which can also be very useful.

The main purpose of the model is to identify beta/risk of a dependent variable against both single factor as well as multi factors.

Thanks in advance!

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    $\begingroup$ First of all, if you're accepting the idea of time varying beta (or beta as function of time), you should use a state-space representation of your regression and solve it via Kalman filter. In that way you can freely use your whole sample and analyze beta time series. If you don't want to follow this way, use different window lengths and make a term structure of beta, then study its shape to make a step forward. $\endgroup$ – Lisa Ann May 7 at 17:07
  • $\begingroup$ Thanks for the comment, @LisaAnn. Due to operational limitations, this does not seem to be a viable option at the moment. That is why I am trying to find proof/reasoning for using short or long history to identify beta of a security. $\endgroup$ – AK88 May 7 at 19:13
  • $\begingroup$ Ok, if you can't use a dynamic linear model then follow my second advice: estimate beta over different rolling windows (from 1 to 10 years of data) and work on that "curve". As instance, you can run PCA and extract the 1st principal component. Or you can just calculate the median and use that. Even the slope of the "curve" could give insights. But please don't stick to a fixed window length parameter, there's no such thing as constant magic numbers in the financial markets. Nowadays, when I read a research paper where constant magic numbers are used to prove something, I usually quit. $\endgroup$ – Lisa Ann May 8 at 8:54

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