# What does it mean to normalize the data by the autocorrelation at the 0-th lag?

I'm just digging into python as a newbie and saw this expression in the plot docs: normalize the data by the autocorrelation at the 0-th lag. I didn't see further details, and Google wasn't very helpful. What exactly does this mean?

I saw this in the acorr() function of Matplotlib Pyplot module here: http://matplotlib.org/api/pyplot_api.html

• In what context is this?
– Andy
Commented May 18, 2015 at 15:21
• @Andy it's in the pyplot docs. I've added the link to my original question. Commented May 18, 2015 at 15:23
• As far as I know, autocorrelation at the 0th lag is always 1, so doesnt make much sense to me ... Commented May 18, 2015 at 15:23
• @kjetilbhalvorsen that's part of what confuses me. Also I thought normalization would have to be specified - e.g. are you just subtracting the mean, or are you dividing by variance, or normalizing in some other way? not sure how you normalize other than subtraction or division of that one other number, since this doesn't seem to refer to a range of lags either. Commented May 18, 2015 at 15:27
• I think they've simply confused aurocorrelation and autocovariance in the comment ... the autocorrelation at lag 1 is 1, but you might normalize the sample autocovariance at lag $k$ by the sample autocovariance at lag $0$ ... getting an estimate of the autocorrelation at lag $k$. When someone writes something you don't understand, the best person to guess what was meant is the person that wrote it. Commented May 19, 2015 at 5:58