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I have a dataset of real estate returns in markets A, B, and C. I also have national returns, denoted market N. I have 10 columns representing the time period for each data point. Market A only has data for periods 1 through 5. Market B only has data for periods 3 through 7. Market C only has data for periods 1 through 9. Market N has data for all periods. Therefore, the only periods where we have data points for ALL markets are periods 3, 4, and 5.

With the above in mind, I want to calculate the betas for each market pair: AN, BN, CN. Disregarding the size of the sample (illustrated as such for simplicity), would it make most sense to calculate beta for each pair using data only from periods 3, 4, and 5? I want to compare betas to each other. I initially calculated beta for each pair based on which periods they themselves as a pair had in common but then realized this may not make sense. If each beta is calculated with different periods, then they are not comparable. Even though we lose out on data the way I explained above, at least we lose out on the same periods across each market pair. Am I making sense? Thank you!

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    $\begingroup$ You have a "missing data" problem. Does this help? quant.stackexchange.com/questions/41683/… $\endgroup$
    – nbbo2
    May 26, 2021 at 23:08
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    $\begingroup$ I think the general question is if it’s compromising to your insights if you delete data. A more simple example is if we have data with holidays. If we delete all data with holidays, then run an analysis, does this compromise the insights? I don’t think so because beta is calculated independent of time, but I am obsessing and stressing on this for some reason. $\endgroup$ May 27, 2021 at 0:26
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    $\begingroup$ Depends on the insights you want to produce. If you want to come up with a trading strategy, you should only use the intersection of all available data sets, i.e. if you want to arbitrate AN vs CN, this is clearly only possible when both A,C, and N are open. $\endgroup$ May 27, 2021 at 9:26
  • $\begingroup$ That’s what I’m thinking. What I initially did was I took each pair and individually reduced those datasets to data points in the periods where both markets had data. Then I realized I’m comparing different sized data. That would’ve been an issue right? $\endgroup$ May 27, 2021 at 14:41

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