How do I test for correlation between digital data series?

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

[Chris]

Nevermind, found a thread: http://stackoverflow.com/questions/3507669/matlab-correlation-number

Answer 1

[Wayne King]

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);

Answer 2

[Wayne King]

The best way is to compute the cross correlation sequence.

The reason you want to do that is with time series data, you want to account for the fact that the two series may differ only by a shift.

   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];
   [c,lags] = xcorr(a,b,'coeff');
   stem(lags,c)

Look at some of the "Examples and How Tos" here

correlation

[Chris]

I get an error when I run that: "Undefined function 'xcorr' for input arguments of type 'char'." Still get an error even if I convert a & b to logicals.

Also, in my case there is no concern about a time shift, does that mean I can use some other method to test for correlation?