Can autocorrelation be greater than one?

  • Thread starter Rib5
  • Start date
  • #1
Rib5
59
0
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].
 

Answers and Replies

  • #2
jrlaguna
107
1
Hm... can't help if you don't tell me how you're computing the autocorrelation...
 
  • #3
morphemera
24
0
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.
 
  • #4
thrillhouse86
80
0
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
 

Suggested for: Can autocorrelation be greater than one?

Replies
1
Views
171
Replies
4
Views
2K
  • Last Post
Replies
8
Views
1K
Replies
2
Views
191
Replies
0
Views
140
Replies
1
Views
681
  • Last Post
Replies
15
Views
787
Replies
2
Views
406
Top