Two different definitions of autocorrelation?


I’m used to the following definition of autocorrelation:

R(\tau) = \frac{<(X_t - \mu)(X_{t+\tau}-\mu)>}{\sigma^2}

However, it looks like acorr is just giving me

R(\tau) = \sum{X_t*X_{t+\tau}}

Just specifying normed=True doesn’t get the first formula. Is there some trivial option that I’ve missed?

Here’s what I did:

It’s easy enough to subtract \mu from my timeseries, but when I ask acorr to normalize things for me, I get the whole timeseries normalized by the value of R(0):

if normed: c/=,x)

I really do want the formula I gave, which requires each point of the autocorrelation to be averaged separately. So, I modified my local version of acorr to say

if normed:
    nrm = arange(len(x))
    nrm = hstack((nrm,nrm[:-1][::-1]))*std(x)**2
    c /= nrm




Michael Lerner, Ph.D.
IRTA Postdoctoral Fellow
Laboratory of Computational Biology NIH/NHLBI
5635 Fishers Lane, Room T909, MSC 9314
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