How to compute sliding or running window correlation coefficient?

Dear colleagues,

 I want to compute the sliding or running window correlation coefficient. I have read related papers, the formula is as following:

t=n,n+1,n+2,n+3，......。 n means the length of silding or running window.

Could you translate this formula into Matlad codes? Any help is very much appreciated! Many many thanks!

[Thomas Koelen]

Have a look at this mfile:

http://www.mathworks.com/matlabcentral/fileexchange/18409-comparing-time-series-using-semblance-analysis

[Roger Stafford]

See my reply at your previous thread:

   http://www.mathworks.com/matlabcentral/answers/195874

Answer 1

[Victor]

For a fast computation you can implement moving sums of X and X^2 for both signals, then obtain moving averages and variances as

M = sum(X)/windowLen;
V = ( sum(X^2) - sum(X)^2 )/windowLen;

Then find sum

V12 =  sum( (X1-M1)*(X2-M2) );

And then sliding correlation itself:

C = V12 / sqrt(V1*V2);

It can be done efficiently within one for loop by adding one new value and substacting the old one.

*The same way we can find statistical moments, by adding moving sums of higher powers - X^3, X^4 etc.

**Additionally, you can add any span value for integer decimation.

Answer 2

[David J. Mack]

If someone encounters this problem, I have written a function in analogy to the MOVSUM function, which compute the moving Pearson correlation:

MOVCORR

Greetings, David