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# Gaussian2.R -- version 2011-03-18
p <- 5L # number of assets
N <- 500L # number of obs
rho <- 0.5 # correlation between two assets
## create uncorrelated observations
X <- rnorm(N * p); dim(X) <- c(N, p)
## check (see ?pairs)
panel.hist <- function(x, ...) {
usr <- par("usr"); on.exit(par(usr))
par(usr = c(usr[1L:2L], 0, 1.5) )
h <- hist(x, plot = FALSE)
breaks <- h$breaks; nB <- length(breaks)
y <- h$counts; y <- y/max(y)
rect(breaks[-nB], 0, breaks[-1], y, ...)
}
pairs(X, xlim = c(-5, 5), ylim = c(-5,5), labels = NA,
diag.panel = panel.hist, col = grey(0.4))
cor(X)
## set correlation matrix
M <- array(rho, dim = c(p, p)); diag(M) <- 1
## induce correlation, check
C <- chol(M); Xc <- X %*% C
pairs(Xc, xlim = c(-5,5), ylim = c(-5,5), labels = NA,
diag.panel = panel.hist, col = grey(0.4))
cor(Xc)
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