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##' Returns the partial cross-quantilogram
##'
##' This function obtains the partial corss-quantilogram and the cross-quantilogram.
##' To obtain the partial cross-correlation given an input matrix, this function interacts
##' the values of the first column and the k-lagged values of the rest of the matrix.
##' @title Paritial Cross-Quantilogram
##' @param DATA1 An input matrix (T x p1)
##' @param DATA2 An input matrix (T x p2)
##' @param vecA A vector of probability values at which sample quantiles are estiamted
##' @param k The lag order
##' @return The partial corss-quantilogram and the cross-quantilogram
##'
##' @references
##' Han, H., Linton, O., Oka, T., and Whang, Y. J. (2016).
##' "The cross-quantilogram: Measuring quantile dependence and testing directional predictability between time series."
##' \emph{Journal of Econometrics}, 193(1), 251-270.
##'
##' @author Heejoon Han, Oliver Linton, Tatsushi Oka and Yoon-Jae Whang
##' @export
crossqreg.partial = function(DATA1, DATA2, vecA, k)
{
## Important idea: make hit first
## Quantile Hit process with demean
matH = qreg.hit(DATA1, DATA2, vecA)
## cross-quantilogram of lag order k
RES = corr.lag.partial(matH, k)
## results
list(CRQ = RES$CRQ, ParCRQ = RES$ParCRQ )
} ## EoF
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