However, correlation is not transitive. That A is correlated with B and B correlated with C tells you very little about the correlation of A with C. (This is an exercise in spherical trigonometry :-)
If A,B,C are three series of numbers of the same length arranged in N triplets, I see a geometrical explanation why correlation should be transitive (it is no trigonometric however).
First high correlation implies points are close to a plane around X axis (and not Y,Z axis), second high correlation implies they are close to a plane around Y axis (and not X, Z axis). The intersection of the two plane is a line unless they are one and the same plane. If it is a line, the third correlation is also pretty high. In order to have the two planes intersect at a very narrow angle (to degrade the 3rd correlation), you need very different orders of magnitude between the standard deviations of the first and second series...
ah OK I get it, this is were you have spherical trigonometry to express the angle in terms of the standard deviation. Forget it. Pierre
This all follows from considering that "covariance" is an "inner product". The Cauchy-Schwarz inequality gives you "covariance is less than the product of standard deviations".
Does that answer your question? Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith
