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# a robust skewness measure described in Kim and White (2004)
rob.sk <- function(x){
if(!is.vector(x)){
x <- as.matrix(x)
nobs <- dim(x)[1]; ndim <- dim(x)[2]; m <- colMeans(x)
sk1 <- numeric(ndim)
sk2 <- numeric(ndim)
for(i in 1:ndim){
# standard skewness
x. <- x[,i]-m[i]; v <- mean(x.^2)
std.x <- x./sqrt(v)
sk1[i] <- mean(std.x^3)
# robustified skewness
quant <- quantile(x[,i], prob=seq(0.25,0.75,0.25))
sk2[i] <- (quant[3]+quant[1]-2*quant[2])/(quant[3]-quant[1])
}
} else {
x <- as.vector(x)
nobs <- length(x); m <- mean(x); ndim <- 1
# standard skewness
x. <- x-m; v <- mean(x.^2)
std.x <- x./sqrt(v)
sk1 <- mean(std.x^3)
# robustified skewness
quant <- quantile(x, prob=seq(0.25,0.75,0.25))
sk2 <- (quant[3]+quant[1]-2*quant[2])/(quant[3]-quant[1])
}
sk <- rbind(sk1, sk2); rownames(sk) <- c("standard", "robust"); colnames(sk) <- paste("series",1:ndim)
sk
}
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