R-help Digest, Vol 2, Issue 13

Subject: [R] Autocovariance and acf
Date: Sat, 12 Apr 2003 05:17:51 +0200
From: christianlederer at t-online.de (Christian Lederer)
Reply-To: lederer at trium.de
To: R-Help <r-help at stat.math.ethz.ch>

Hi,

i calculated the autocovariance of a vector x of length n, using

        result <- acf(x, lag, type="covariance")

and expected, that result$acf would contain the values
cov(x,x), cov(x[1:(n-1)], x[2:n]) ...

However, acf does not calculate this covariances. Instead
of cov(x[1:(n-i)], x[(i+1):n]) i am getting

        ( (x[1] - m) * (x[i+1]-m) + ... + (x[n-i]-m) * (x[n]-m) ) / n

where m = mean(x).

I anderstand, that for efficiency reasons only the mean of the whole
vector x is substracted instead of the means of the partial vectors.
But why does it divide by n instead of n-i?

Christian