[R] quantreg Wald-Test

[stefan23]

Dear all,
I know that my question is somewhat special but I tried several times to
solve the problems on my own but I am unfortunately not able to compute the
following test statistic using the quantreg package. Well, here we go, I
appreciate every little comment or help as I really do not know how to tell
R what I want it to do^^
My situation is as follows: I have a data set containing a (dependent)
vector Y and the regressor X. My aim is to check whether the two variables
do not granger-cause each other in quantiles. I started to compute via
quantreg for a single tau:= q:
rq(Y_t~Y_(t-1)+Y_(t-2)+...+X_(t-1)+X_(t-2)+...,tau=q) 
This gives me the quantile regression coefficients. Now I want to check
whether all the coefficients of X are equal to zero (for this specific tau).
Can I do this by applying rq.anova ? I have already asked a similiar
question but I am not sure if anova is really calculating this for me..
Currently I am calculating
fitunrestricted=rq(Y_t~Y_(t-1)+Y_(t-2)+...+X_(t-1)+X_(t-2)+...,tau=q) 
fitrestrited=rq(Y_t~Y_(t-1)+Y_(t-2)+...,tau=q)
anova(fitrestricted,fitunrestricted)
If this is correct can you tell me how the test value is calculated in this
case, or in other words:
My next step is going to replicate this procedure for a whole range of
quantiles (say for tau in [a,b]). To apply a sup-Wald-test I am wondering if
it is correct to choose the maximum of the different test values and to
simulate the critical values by using the data tabulated in Andrees(1993)
(or simulate the vectors of independent Brownian Motions)...please feel free
to comment, I am really looking forward to your help!
Thank you very much 
Cheers
Stefan




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