Interpreting xcorr results compared to corrcoef

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JM
JM 2019-8-16
编辑： zmkal 2024-1-14
I am having trouble understanding why I am getting different outputs when using coeff and a normalized xcorr, specifically at 0 lags.
Shouldn't 0 lags produce the same r value when using an xcorr compared to coeff since the time series is matched up in both cases?
Note - I am using "coeff" because the two sets of data are equal in length, but the ampltitudes are much different.
Below illustrates the example:
I have two sets of data (A and B) that are 1000 datapoints each.
I use corrcoef(A,B) and then I use xcorr(A,B,500,'coeff").
corrcoef outputs a single value that is rather low such as r = 0.15.
xcorr outputs r values at lags -500 to 500, and they are all higher than r = 0.15.
However my question is, shouldn't r at 0 lag be = 0.15 since the data is already lined up in time?

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David Goodmanson
David Goodmanson 2019-8-17
Hi Jonathan,
For the input column vectors, corrcoeff subtracts the mean off of each one and normalizes each to be a unit vector. xcorr with the 'coeff' option normalizes, but doesn't subtract off the mean.
a = (1:1000)';
b = mod((a.^(4/3)),1000);
corrcoef([a b])
ans =
1.0000 0.1745
0.1745 1.0000
xcorr(a,b,0,'coeff') % zero lag only
ans =
0.7865
aa = a-mean(a);
bb = b-mean(b);
xcorr(aa,bb,0,'coeff')
ans =
0.1745 % agrees
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David Goodmanson
David Goodmanson 2020-5-7
编辑：David Goodmanson 2020-5-7
Hello SZ, thanks for the comment. it's good to hear that a blast from the past still might be useful.
zmkal
zmkal 2024-1-12
编辑：zmkal 2024-1-14
Hi @David Goodmanson, still helpful but has raised a few new questions for me.
Maybe someone or you can help?
First, I calculated an autocorrelation function using xcorr:
[akf, lags] = xcorr(A-mean(A), 'coeff');
and secondly via corrcoef:
B = A;
for i = 1:length(A)-1
B = circshift(B,1);
R = corrcoef(A,B);
corr(i,1) = R(2,1);
end
Of course, the first variant also shifts the function in the negative direction and the second variant only in the positive direction in the way I implemented it. However, from what I read above, I would have expected the functions to look the same in the range of the positive shift?
But they do not ....

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