I did some computation lately and found the following results about correlations. These results show me something I did not realize before.

Given time series A, B and C. Say Corr(A, B)=0.2, and Corr(A, C)=0.05. With this, one would think that to help understand A, C is useless. But that is not always the case. If one combines B and C and gets series D, where D = B & C, one may find Corr(A, D)=0.3, which means C actually can be very valuable in studying A. This can be understood as the combination of B and C and can eliminate some elements in both B and C that are negatively correlated with A.

Would anyone share further lessons on this?

Alex Castaldo adds:

Before I read this I had not realized that correlation is not transitive (i.e. if A is correlated to B, and B is correlated to C, it does not follow that A is correlated to C). It does not directly answer your question, but it shows that the behavior of correlation can be rather unintuitive.


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