Compute the Cross-correlation coefficient out of one Vector

Hello everyone,

I got one vector with 100000 random numbers (100000X1) that each value is at a different time - representing a random process.

I need to calculate the Cross-correlation coefficient without using the "corr" function between the original process and the time-transmitted procedures, 0 to 15-time shifts. (Between x [t] and x [t + k], k = 0,1, ... 15).

I was thinking of using a for loop to make 14 more different Vectors and make them all one matrix and then calculate the Cross-correlation coefficient.

but I don't know to make those 14 different vectors, also - I don't know if that is the right way to do it.

Thank you.

Answer 1

[Alan Stevens]

If your data is in a vector V, then the following should do it:

coeff = zeros(1,16);
for k = 1:16
    lag = k-1;
    
    v1 = V(1:end-lag);  
    v2 = V(k:end);
    
    v1scaled = (v1 - mean(v1))/std(v1);
    v2scaled = (v2 - mean(v2))/std(v2);
    
    coeff(k) = v1scaled'*v2scaled/(n-1);
      
end

[Jacob Shamir]

Thank you very much :)