Recursive time-series regression and storing results (HAVING TROUBLE WITH RESIDUALS)

Hello community!

I write to you because I am having trouble with a piece of code for my master thesis.

I am trying to recursively regress two 200x273 matrices (regress column 1 of A on column 1 of B, column 2 of A on column 2 of B and so on....)

I am especially having trouble extracting the residuals of each observation in each regression: concretely, as output I would like:

A vector 273x1 of Betas (estimates)

A vector 273x1 of Alphas (constants)

A matrix 200x273 of residuals

A table of descriptive stats (r^2, p-values etc.) for each of the 273 regressions

This is the code as I have it now:

for i = 1:size(volatility_TEST_e, 2)

for k = 1:size(volatility_TEST_e, 1) Not sure about this

% Get the ith column of volume

Y = vol_firms_time_frame_TEST_e(:,i);

% Get the ith column of volatility

X = [ones(200,1), volatility_TEST_e(:,i)];

[b,r] = regress(Y,X);

Output_Alpha(i,:)=b(1,:)

Output_Beta(i,:)=b(2:end,:);

Output_Residual(i,k)=r(1:end,k); This doesn't work

end

end

I have successfully accomplished outputs 1 and 2, but need help for 3 and 4.

Cheers!

Giorgio