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Mmm, noo? By compressing it, first by MA and then by log, you're stripping it of variation. So I suspect you get this stupidly high r-squared result pretty artificially
It just goes to your point about interpretation. Provided the variable is described accurately, the amount of variation explained is whatever it is and you can note that it’s not particularly impressive because of how the variable was constructed.
To me, it’s not very important because the relationship passes the eye test so dramatically.
Someone predicted the power law trend almost a decade ago and it’s largely held.
Fine, it works in practice but does it work in theory?!
If it works in practice, then it inherently works in theory...we just have to figure out what that theory is.
Sometimes you observe the empirical regularity before you understand its reason.
I don’t see any inherent reason why using log prices is inappropriate or why you can’t use R-squared, it’s just that you’re explaining the variation in the log-prices.