[R] Autocovariance and acf

Christian Lederer christianlederer at t-online.de
Sat Apr 12 05:17:51 CEST 2003


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?


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