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##' The correlation statistics for a given lag order
##'
##' The function obtains the simple correlation statistics. The values in the first column of input matrix
##' is interacted with the k-lagged values in the second column.
##' @title Correlation Function
##' @param matH The matrix with the column size of 2
##' @param k The lag order (integer)
##' @return Correlation
##'
##' @author Heejoon Han, Oliver Linton, Tatsushi Oka and Yoon-Jae Whang
corr.lag = function(matH, k)
{
## size
Tsize = nrow(matH) ## =: T
Nsize = Tsize - k ## =: N
## {H_1t, H_2t-k}
matD = matrix(0, Nsize, 2) ## N x 2
matD[,1] = as.matrix(matH[(k+1):Tsize, 1])
matD[,2] = as.matrix(matH[ 1:Nsize, 2])
## the following matrix contains inner-products of two vectors in H.
matDD = t(matD) %*% matD ## 2 x 2
## cross-quantilogram of lag order k
CRQ = matDD[1,2] / sqrt( matDD[1,1] * matDD[2,2] ) ## 1 x 1
## list
return(CRQ)
} ## EoF
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