exponential of Covariance of two variables in logs, cov(X,Y)=exp(X)exp(Y)cov[ln(X),ln(Y)]

Asked Jul 17 '18 at 20:13

Active Jan 30 '21 at 20:26

Viewed 394 times

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

edited Jan 30 '21 at 20:26

asked Jul 17 '18 at 20:13

vanbasten

1

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. – within_person Jul 17 '18 at 20:18
This is trivially true for degenerate random variables (i.e. constants), since $ \text{Cov}(X, Y) = 0 $ if they are real numbers ;) – Kevin Li Jul 17 '18 at 20:22

exponential of Covariance of two variables in logs, cov(X,Y)=exp(X)*exp(Y)*cov[ln(X),ln(Y)]