# Can autocorrelation be greater than one?

I have to find the autocorrelation of a random variable. When I compute the theoretical autocorrelation I get the result where it is [1 -2 3 -2 1] centered around zero, and zero everywhere else.

I tried estimating the autocorrelation of the random variable using

ryy_est = xcorr(Y,20, 'unbiased');

in Octave, and I get the exactly same distribution. Can anyone explain to me what is going on? I was under the impression that a correlation can't be greater than 1. I've though about just dividing everything by 3, since it is equal to 3 at m = 0, however I don't know if this would be right, and I still don't know why I am getting values like that.

The random variable is a gaussian random variable of zero mean and unit variance, put through a filter y[n] = x[n] - x[n-1] + x[n -2].

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Hm... can't help if you don't tell me how you're computing the autocorrelation...

Usually, the autocorrelation function is defined to be normalized so that its value should be in the -1 and 1. The things that you should check is the exact definition of the function xcorr. Don't blindly guess the meaning of a function, cos they usually do not use the standard definition with some reason such as efficient.

I think the problem is that the autocorrelation function in most definitions is normalised by dividing through by the variance (or the product of the standard deviations at the times of interest if its not a covariant stationary process).

The function xcorr doesn't normalize the resulting autocorrelation function by this variance. If you want it to do that you need to go:
ryy_est = xcorr(Y,20, 'unbiased','coeff')

Can someone verify that this is true ?

Regards,
Thrillhouse