Granger Causality Test

i think your two statements deserve separate answers.

1)

granger causailty is only used ( as far as i know ) in the context of 
deciding on which variables in a previusly estimated VAR cause another
in the granger sense. ( defined in Lutkepohl ) . But, since it's a n 
already estimated VAR,  you should have already decided whether the
series under study needed to be differenced or not in order that the VAR 
estimation is done on variables that are stationary.

So, granger causality doesn't really have much to do with stationarity, 
I don't think,  because that should have been worked out during the
estimation fo the VAR.

2)

in the 70's before cointegration was discovered, people used to 
difference time series variables in order to make them stationary (
for example , if they were prices, they would make them differenced 
prices ). but, it was realized that, if one did this, then the 
information about levels of the
series was lost and it was always felt that there must be a better 
approach so the levels info was not abruptly discarded.

then, engle and granger figured out in the early 80's that there were 
cases where two variables could be non-stationary and yet
the regression of the two on each other could still be valid 
statistically ( cointegration ). So, they were able to figure out a way 
to
keep the levels in the specification by rewriting the regression 
relationship in the form of an error correction model. This was then 
extended beyond the
bivariate case to what is called a vector-error correction model ( VECM 
) which is like a VAR but slightly different and I couldn't do the 
description  of a VECM justice even if  i tried so I won't.

There is a lot of econometrics literautre in this area that talks about 
this in a much more eloquent way than I could.

Some good books in order of increasing difficulty ( atleast to me ).

Enders
Zivot ( S+Finmetrics book )
Hayashi
Lutkepohl
Hamilton

To me, Hamilton and Lutkpohl are similar in difficulty and require a 
larger time investment than the others.  Enders is the most basic but it 
gives nice intuition and is good for an intro. Zivot is more general in 
that it covers various  time series topics but also provides a brief but 
nice discussion on the topics above.

Granger Causality Test

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