Correlation is a measure of linear dependence between two random variables. So no additional variables are involved in the calculation of the correlation between v X and Z, and also, in principle these variables may be just random variables and not time series.

Granger causality is a concept of marginal predictability. So here the time dimension of the potential relationship between X and Z is important. That is why we usually use the time index to denote X(t) and Z(t) as time series.

The definition of Granger causality is a little confusing because is a definition of absense of Granger causality!!! Anyhow, the important thing is that X Granger causes Z, if the lags of X(t) ( meaning X(t-1), X(t-2), X(t-3), etc..) have the ability to predict Z(t) even beyond the predictability contained in the own lags of Z(t).

Notice that a correlation is a symmetric object: Correlation between X and Z is the same as Correlation between Z and X. Granger causality needs not to be symmetric!!! X can Granger cause Z but not the other way around.

Clive Granger noted that economic causality involved the time dimension. If X causes a disaster, let´s say, X must happen before the disaster takes place. He then created this concept of Granger causality as a notion of predictability. It does not mean fundamental or economic causality, it just means predictability.

Hope it helps!

Thank you so much Sir for the answer..

In a simple statement, correlation measures relationship between simple regression model (a static mode at some points) i.e. between variables X and Y as the case maybe, while causality test is meant to check which variable Granger cause one another, also note that Granger test can be conducted both on simple and multiple models, basically to look at the direction of causality, which might be either bi-directional or uni-direction since it is a dynamic model. Hope you better informed by now!

The correlation between variables is 0.79, which is too high; explain it based on the concept causality / granger causality. What would be the answer of this particular question please