MATLAB: Multivariate regression betas stock returns

betafor loopMATLAB and Simulink Student Suitemultivariatenot workingregressionreturnsrollingstock returnsus stock returns

I have a matrix of stock returns, 4280 (rows) by 7379 (columns).
I need to regress the 1st to 15th cell in column 3 (1,3) against the 1st to 15th cells in columns 1 and 2 (1,1), (1,2).
Then the 2nd to 16th cell in column 3 (2,3) against the 2nd to 16th cells in columns 1 and 2 (2,1) and (2,2) etc. So like a rolling window.
The columns remain constant, but each variable window (i:i+14) goes down by one row.
Once the whole column is done, it needs to go back up to the 4th column, but continue regressing against columns 1 and 2. Then the 5th column against columns 1 and 2, etc.
This is the code I have so far:
Nwin = 15;                                                              % set window for rolling regression
betasMkt  = ret.*NaN;   betasMkt(:,1)  = ret (:,1);       % initialize empty matrix for Market betas
betasDisp = ret.*NaN;   betasDisp(:,1) = ret (:,1);       % initialize empty matrix for CSAD betas
for j = 1:size(ret,2)-2
  for i = 1:size(ret,1)-Nwin
    vars = [ret(i:i+Nwin-1,j+2) ret(i:i+Nwin-1,1) ret(i:i+Nwin-1,2)]; 
    vars = vars(~isnan(vars(:,1)),:);
    vars = vars(~isnan(vars(:,2)),:);    
    vars = vars(~isnan(vars(:,3)),:);
    if size(vars,1) > 15
      y                     = vars(:,1);
      x                     = [ones(rows(y),1) vars(:,2:3)];
      b                     = regress(y,x);
      betasMkt(i+Nwin,j+2)  = b(2,1);                                         % market beta
      betasDisp(i+Nwin,j+2) = b(3,1);                                         % dispersion beta
    end
  end
end
However, the betasMkt and betasDisp outputs are both just column 1 of 'ret'. It doesn't seem as if any regression has been performed.
Could anyone see where I am going wrong please?
I desperately need to figure this out soon.
Thank you for your time

Best Answer

OK, just add as new Answer since preceding getting rather long...try this out; seems to work ok here on the sample dataset.
NB: The one place had logic error before (and you should have gotten an indexing error out of bounds owing to it that would be why only had one column because it died at end of first j loop) is that the row indices initialization was outside both loops, not before the i loop to start over after having done the initial set of all columns.
ret=xlsread('MultivariateExample.xlsx'); % read the data, shorten variable names
[r,c]=size(ret);                         % size of the data r(ows), c(olumns)      
nWin=15;                                 % window length
nOK=10;                                  % minimum finite observations required
betasMkt=nan(r-nWin,c-2);                % initialize NaN matrix for Market betas
betasDisp=betasMkt;
for j=1:c-2
  i1=1;                                  % initialize index variables each column pass
  i2=nWin;
  for i=1:r-nWin
    vars=ret(i1:i2,[j+2 1:2]);
    vars(any(isnan(vars),2),:)=[];       % make sure all observations finite
    nobs=size(vars,1);                   % how many were ok
    if nobs>nOK                          % how many required to be -- 10
      b= regress(vars(:,1),[ones(nobs,1) vars(:,2:3)]);
      betasDisp(i,j)=b(2);
      betasMkt(i,j)=b(3);
      i1=i1+1; i2=i2+1;                  % increment counters
    end
  end
end
NB:
I indexed the output arrays by 1:C-2 and 1:R-nWin so the actual third column results are the first set of coefficients. Not much point in keeping two columns of NaN simply to account for a column offset of a constant.
If you do need to know which actual set of indices built each weighted set of coefficients, I'd keep another auxiliary variable (say the value of i1 would be appropriate) along with the coefficients. You could also keep nObs as a second. Those two would be good candidates for the first two columns and you could then go back to a full-column array size. :)
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