Fast rolling correlation in Matlab
I am trying to get a function to calculate the move / roll correlation for two vectors and speed is high priority since I need to apply this function in an array function. I have (which is too slow):
Data1 = rand(3000,1);
Data2 = rand(3000,1);
function y = MovCorr(Data1,Data2)
[N,~] = size(Data1);
correlationTS = nan(N, 1);
for t = 20+1:N
correlationTS(t, :) = corr(Data1(t-20:t, 1),Data2(t-20:t,1),'rows','complete');
end
y = correlationTS;
end
I think that the loop for
could be done more efficiently if I knew how to create roling window indexes and then apply accumarray
. Any suggestions?
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1 answer
Following @knedlsepp's advice and using a filter like in movingstd , I found the following solution, which is pretty fast:
function Cor = MovCorr1(Data1,Data2,k)
y = zscore(Data2);
n = size(y,1);
if (n<k)
Cor = NaN(n,1);
else
x = zscore(Data1);
x2 = x.^2;
y2 = y.^2;
xy = x .* y;
A=1;
B = ones(1,k);
Stdx = sqrt((filter(B,A,x2) - (filter(B,A,x).^2)*(1/k))/(k-1));
Stdy = sqrt((filter(B,A,y2) - (filter(B,A,y).^2)*(1/k))/(k-1));
Cor = (filter(B,A,xy) - filter(B,A,x).*filter(B,A,y)/k)./((k-1)*Stdx.*Stdy);
Cor(1:(k-1)) = NaN;
end
end
Compared to my original solution, the runtime is:
tic
MovCorr(Data1,Data2);
toc
Elapsed time is 1.017552 seconds.
tic
MovCorr1(Data1,Data2,21);
toc
Elapsed time is 0.019400 seconds.
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