Granger Causality in Quantiles

Good Day dear community,

I am currently working on a causality test (Granger Causality in Quantile) and can't find any good help online. I am using two timeseries with daily data and length of 115. Unfortunately in don't know how to solve the issue in R.

I started with:


y <- diff(log(xbtc1))
q <- seq(0.1,0.9,0.1)
tn <- length(y)-1
ya <-y[1:tn]
yn <-y[2:(tn+1)]
x <- diff(log(gxbt))

Lag length is 1 (Using AIC and BIC)

Than I used the quantile regression function:

test3 <-rq(yn~ya+x[1:tn], tau = q)
test2 <- rq(yn~ya, tau = q)

So I assume that x has an signifficant influence since 0 isn't part of the confidence interval for most quantiles, but ya isn't signifficantly different from 0.

So the question is:
Is this even the correct way of testing for granger causality in quantiles? Since I couldn't find any code online to orientate on, I just started trying things out by myself.

Is it enough to show in test3 that the lagged x has a significant impact on yn, so that you can say x is granger causing yn in the specific quantile?

Hope you can understand my english,

Best regards Robbymo

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