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

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Jiazeng Shan 2011-7-12

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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 2011-7-12

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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 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 2011-7-15