How can I estimate a Vector Autoregressive (VAR) Model by OLS?

How can I estimate a VAR Model with the vgxvarx function by Ordinary Least Squares ( OLS )?

By default vgxvarx uses the Maximum Likelihood and I can't find how to change it.

I tried with the default MLE:

Spec = vgxset('n',5,'nAR',1,'Constant',false);
EstSpec = vgxvarx(Spec, Y, [], Y0);

but I get this error:

Error using mvregress (line 425)
Covariance is not positive-definite.

Error in vgxvarx (line 521)
    [x,Q,~,xvar] = mvregress(D,R, 'covtype',covartype, 'varformat',varformat, ...

Here:

http://www.mathworks.co.uk/help/econ/vgxvarx.html

it mentions to set 'MaxIter' to 1 for OLS, but it's not clear how to use the OLS approach.

[Shashank Prasanna]

Would you be willing to share why you don't want to use the MLE approach in the Econometrics toolbox?

[Valentina]

Because with MLE I get the above-mentioned error, while I was able to estimate the model with the same data, using a function in the R software that uses OLS.

Answer 1

[Hang Qian]

Yes, estimation of a VAR(p) model by OLS is possible using the vgxvarx functionality. The vgxvarx uses maximum likelihood for rigorous treatment of missing values and presample values.

If the data are complete and presample values are specified (using the first p values of the data), vgxvarx will produce an estimator identical to the OLS estimator. For example, consider a VAR(2) model with 3 variables,

Y = rand(100,3);

Spec = vgxset('n',3,'nAR',2);

EstSpec = vgxvarx(Spec,Y(3:100,:),[],Y(1:2,:));

OLS1 = [EstSpec.AR{1},EstSpec.AR{2}]'

OLS2 = [Y(2:end-1,:),Y(1:end-2,:)] \ Y(3:end,:)

The second estimator is the raw OLS estimator.

norm(OLS1-OLS2) suggests that vgxvarx reproduces the raw OLS estimator.

Hang Qian

[Spyridon Kariofylis]

Does this still work in 2020 edition?