Oliver Faulhaber wrote: > 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? > > The latter. If you think a little closer, you'll realize that sum(X.return) is going to be pretty close to X[1000000], except for the sum of at most 999 terms (at most 961, actually). You then proceed to calculate the mean by dividing by the number of terms which is essentially 1/i.
> Thanks for any enlighting > replies in advance > Oliver > > ______________________________________________ > R-help@stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.