One factor model calibration

How can I add more common factors in a One factor model?

I have implemented the code from here (https://it.mathworks.com/help/risk/examples/one-factor-model-calibration.html) . I tried to modify the "fitlm" arguments in the for loop adding another time series for a second common factor:

for i = 1:4

    lm = fitlm(commonfactor1,commonfactor2,dependentVar(:,i));
    w_regress_std(i) = lm.Coefficients{'x1','x2','Estimate'};

end

I get this error.

"Error using classreg.regr.TermsRegression.createFormula (line 758) The model definition must be a formula character vector, a terms matrix, a model alias, or a LINEARFORMULA."

Thank you

Answer 1

[Max Wyse]

Hi Giacomo,

It looks like you are trying to fit a linear regression model using two independent variables. I can adjust your for loop to make this work like so:

rng(1,'twister')
commonfactor1 = rand(200,1);
commonfactor2 = rand(200,1);
dependentVar = rand(200,4);

%this should work
for i=1:4
    lm = fitlm([commonfactor1, commonfactor2],dependentVar(:,i));
    Coeffs(i,:) = lm.Coefficients{{'x1','x2'},'Estimate'};
end

The changes I made to your code are as follows:

1.) I initialzed your variables (I don't have your data)

2.) I passed in all the dependent variables as a matrix, rather than each variable as a separate vector. This is the format expected by fitlm.

3.) I changed 'x1','x2' to {'x1','x2'}. The idea is that the first input in lm.Coefficients are the rows that are to be selected, the second input are the columns. As such, {'x1','x2'} both need to be given in the first input.

4.) I changed w_regress_std(i) to Coeffs(i,:). I did this for two reasons. The first is that you are now pulling out two coeffiecents instead of one, so I want the Coeffs output to be 2 dimensional. The second is that I am not sure what assumptions are going into the calculation of w_regress_std. All I have done is change this code to succesfully compute a multilinear regression, the mathematics in the example you link to may not hold in the 2 dimensional case (I haven't checked).