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This question already has an answer here:

I am stuck in calculating steady state in a model that has covariances in logs. I am wondering in general if the following accurate.

cov(X,Y)=exp(X)*exp(Y)*cov[ln(X),ln(Y)]

if that is accurate could you please let me know which theorem/textbook could be useful?

Thanks a lot and wish you a nice evening

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marked as duplicate by whuber Jul 17 '18 at 23:38

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    $\begingroup$ That formula can't be right. For one thing, ${\rm cov}(X,Y)$ is a scalar and the thing on the right hand side is a random variable. $\endgroup$ – within_person Jul 17 '18 at 20:18
  • $\begingroup$ This is trivially true for degenerate random variables (i.e. constants), since $ \text{Cov}(X, Y) = 0 $ if they are real numbers ;) $\endgroup$ – Kevin Li Jul 17 '18 at 20:22