MATLAB: How to test for correlation between digital data series

correlation

This may be a dumb question. I have two digital data series:
a = [-1 1 -1 -1 -1 1 1 -1 -1 -1 1 1]; b = [1 -1 1 -1 1 1 -1 -1 -1 -1 1 -1];
What's the best way to determine whether they are correlated? Corr? Chi-square? If chi-square, how exactly (there are several functions)?
Thanks

Best Answer

xcorr() is in the Signal Processing Toolbox. You can calculate the cross correlation in the frequency domain and then invert.
   a = [-1 1 -1 -1 -1 1 1 -1 -1 -1 1 1]; 
    b = [1 -1 1 -1 1 1 -1 -1 -1 -1 1 -1];
    npad = length(a)+length(b)-1;
    crosspec = fft(a,npad).*conj(fft(b,npad));
    xcr = fftshift(ifft(crosspec));
    anorm = norm(a,2)^2;
    bnorm = norm(b,2)^2;
    xcr = xcr./sqrt(anorm*bnorm);
    lags = -length(a)+1:length(a)-1;
    stem(lags,xcr,'markerfacecolor',[0 0 1])
Or you can use corrcoef() -- again this is not the best for time series.
 R = corrcoef(a,b);
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