Hi all,
in order to verify some results I did the following test in R (2.4.1.,
windows system):
X <- cumsum(rnorm(1000000))
for (i in 1:1000) {
tmp <- seq(1,length(X),by=i)
X.coarse <- X[tmp]
X.return <- diff(X.coarse)
X.scale.mean[i] <- mean(X.return)
}
plot(X.scale.mean,type="l")
As X is a random walk with increments following a standard normal
distribution, the mean of X should be 0. Further more, each "piece" of
the random walk should also have zero mean - independent of its length.
Why is it then, that the plot of X.scale.mean shows a clear linear trend?
Is the generation of the random walk in some way biased or do I just
miss some point?
Thanks for any enlighting
replies in advance
Oliver
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