Granger causality

I have a variable $A$ which Granger causes a variable $B$, and a variable $C$, separately.

Since A and B are very similar in nature, I should expect that $B$ granger caused $C$ as well. Anyway when I perform the test I can't reject the null hypothesis of no causality between them.

Am I missing by any chance something about the theory and the "math" behind the test?

• Why do you think this is true? And can you come up with a counter-example where it is false? Also read the wiki on the self-study tag and figure out if adding it is appropriate. – Matthew Gunn Nov 5 '16 at 6:35
• Since the statement (1) "$A$ Granger-causes $B$ and $C$" refers to $B$ and $C$ symmetrically--they can be interchanged without changing the meaning at all--then if you could conclude "$B$ Granger-causes $C$" then you could also conclude "$C$ Granger-causes $B$". These two statements allow you logically to deduce that $B$ and $C$ "Granger-cause" each other. (Note that the actual meaning of "Granger-causes" is irrelevant to this argument.) Does it make sense that statement (1) could imply such a conclusion? – whuber Nov 5 '16 at 21:55
• I'm sorry, I have miswritten my question. I meant that A causes B, and A causes C but separately. In other words, I perform two different test in which I verify the causality between and A and B and between A and C. – James Nov 8 '16 at 21:00
• I was going through my old answers and noticed this one was not accepted. Do you perhaps need further clarification? – Richard Hardy Feb 24 '17 at 14:17

• Take the simplest VAR model -- a VAR(1) -- for a trivariate system and see what minimal restrictions are sufficient for $A \not\xrightarrow{Granger} \{B,C\}$.
• Consider whether these restrictions imply $B \not\xrightarrow{Granger} C$.