How to estimate the auto-correlation function value r(k)=E[X(n)X(n-k)]

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Jiazeng Shan
Jiazeng Shan 2011-7-12
If X(n) is an available time series, I want to estimate the auto-correlation function value of r(k). The definition of r(k) is r(k)=E[X(n)X(n-k)]. Should I use the command "xcorr(x)"? But I will obtain a sequence, how could I get a value? Is this way right? I define y(n)=x(n-k), and use the xcorr(x,y)? But still I need a value and how to do the time delay process y(n)=x(n-k)?

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Nirmal Gunaseelan
Nirmal Gunaseelan 2011-7-12
XCORR will return the autocorrelation values and the associated lags at which these values were calculated. The examples section has one:
ww = randn(1000,1);
[c_ww,lags] = xcorr(ww,10,'coeff');
stem(lags,c_ww)
What do you mean by just one value representing ACF? The sequence of values represent correlation between values at different lag indices (time) and a single value does not make sense.
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Jiazeng Shan
Jiazeng Shan 2011-7-12
Yes, that is what I need. I want the ACF value when lag are 0, 1 and so on. If the definition r(1)=E[X(n)X(n-1)],should I use xcorr(ww,10,'biased') instead of xcorr(ww,10,'coeff')? How to determine the options? Thanks.
Nirmal Gunaseelan
Nirmal Gunaseelan 2011-7-15
Option depends on what you want - the document clearly gives the various options and default (none) should work for most cases.

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