Correlation between first and third variable

Question

Let's say we have correlation between x and y as corr(x,y) and correlation between y and z as corr(y,z). What can be said of the correlation between x and z i.e. corr(x,z)?

Thank you for reading.

Answer 1

I don't think you can say much.

The correlation function is not even transitive - in other words if both corr(x,y) > 0 and corr(y,z) > 0, you can't say if corr(x,z) > 0, = 0 or < 0, unless those 2 correlations are especially high (corr(x,y)2+ corr(y,z)2) > 1)...

See for example this article: ftp://163.25.117.117/gyliao/TODylan/Is%20the%20Property%20of%20Being%20Positively%20Correlated%20Transitive.pdf

(for some reason I can't insert a clickable link)