rollmeanRle <- function (x, k)
{
n <- length(x)
cumsum(c(Rle(sum(window(x, 1, k))), window(x, k + 1, n) - window(x, 1, n - k))) / k
}
rollvarRle <- function(x, k)
{
n <- length(x)
means <- rollmeanRle(x, k)
nextMean <- window(means, 2, n - k + 1)
cumsum(c(Rle(sum((window(x, 1, k) - means[1])^2)),
k * diff(means)^2 - (window(x, 1, n - k) - nextMean)^2 + (window(x, k + 1, n) - nextMean)^2)) / (k - 1)
}
rollcovRle <- function(x, y, k)
{
n <- length(x)
meanX <- rollmeanRle(x, k)
meanY <- rollmeanRle(y, k)
nextMeanX <- window(meanX, 2, n - k + 1)
nextMeanY <- window(meanY, 2, n - k + 1)
cumsum(c(Rle(sum((window(x, 1, k) - meanX[1]) * (window(y, 1, k) - meanY[1]))),
k * diff(meanX) * diff(meanY) - (window(x, 1, n - k) - nextMeanX) * (window(y, 1, n - k) - nextMeanY) + (window(x, k + 1, n) - nextMeanX) * (window(y, k + 1, n) - nextMeanY))) / (k - 1)
}
rollsdRle <- function(x, k)
{
sqrt(rollvarRle(x, k))
}
rollcorRle <- function(x, y, k)
{
rollcovRle(x, y, k) / (rollsdRle(x, k) * rollsdRle(y, k))
}