How to vectorize this loop ?

I have a time series of X and Y variables and I want to run a linear regression on it based on a specific time window length. This ends up giving me a time series of regression coefficients. My current implmentation using a loop to picking out data and running a regression on it. How can I vectorize this piece of code?

window_length = 10;
regression_coeff = [];
for i =1:length(X) - window_length 
   regression_coeff = [regression_coeff; regress(Y(i:i+window_length ),X(i:i+window_length )];
end

Answer 1

[Teja Muppirala]

You are calling regress with two vectors. That is the same as a projection using the dot product. So then your code could be written like this:

window_length = 10;
W =ones(window_length+1,1);
regression_coeff = conv(X.*Y,W,'valid')./conv(X.^2,W,'valid');

Answer 2

[George Papazafeiropoulos]

window_length = 10;

X(X==0)=Inf;

X_2=repmat(X,1,length(X)-window_length);

X_3=triu(X_2,-window_length)-triu(X_2,1);

X_4=reshape(X_3,length(X)*(length(X)-window_length),1);

X_4(X_4==0)=[];

X_4(X_4==Inf)=0;

X_5=X_4(~isnan(X_4));

Xfinal=reshape(X_5,1+window_length,length(X_5)/(1+window_length));

Y(Y==0)=Inf;

Y_2=repmat(Y,1,length(Y)-window_length);

Y_3=triu(Y_2,-window_length)-triu(Y_2,1);

Y_4=reshape(Y_3,length(Y)*(length(Y)-window_length),1);

Y_4(Y_4==0)=[];

Y_4(Y_4==Inf)=0;

Y_5=Y_4(~isnan(Y_4));

Yfinal=reshape(Y_5,1+window_length,length(Y_5)/(1+window_length));

regression_coeff = diag((Xfinal./repmat(sum(Xfinal.^2,1).^(1/2),1+window_length,1))'*Yfinal)./(sum(Xfinal.^2,1).^(1/2))';

Best regards,

George Papazafeiropoulos

[Jan]

Please, George, add the links to your profile, but not in your answers.

[George Papazafeiropoulos]

OK Jan, I removed them. Sorry for the inconvenience.