New answers tagged statistics
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first: if he should regress returns then this is actually what he is doing since $ln(p_t)$ is equal to $r_t$ almost surely
then, you put just prices to regression equation and coefficients tell you exactly what proportions are making this linear combination stationary, if they are : p
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This is probably not a good question for Q.SE—despite its application in your strategy, you're (perhaps unaware) asking a general math question: the difference between the ratio of means and the mean of ratios. There are numerous results online that distinguish the difference, but I assume the terminology wasn't apparent to you at the time. I've come ...
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