maximum likelihood estimators

[TomDoan]

Hi Tom,
Thanks a lot, it's clear.
May i come back to the PB3.13 from Lütkepohl:
Use the adjusted-mean form of the VAR(1) model and estimate the
*the coefficients .Assume that the data generation process is Gaussian and
*estimate covariance matrix of the asymptotic distribution of the ML estimators


You said:

You run the VAR by least squares on the mean-adjusted data without a CONSTANT in the regression. The full covariance matrix would be

Code: Select all

disp %kroneker(%sigma,%xx)

I'm fine with the demean problem,this is clear, but

Code: Select all

disp %kroneker(%sigma,%xx)

this code is about the estimate covariance matrix of the asymptotic distribution of the ML estimators ?

Yes.

What i understand is that this cov matrix is ralated to the demean form of the VAR but still with the ols estimates,and as you said "You run the VAR by least squares on the mean-adjusted data without a CONSTANT in the regression". So OLS and ML Estimators are asymptoticaly identicals based on the subsection of the Lütkepohl 's book p.90 subsection 3.4.3 Properties of the ML Estimators
Is it correct?
Thanks for the clarification Tom

That's correct. The ML estimator (conditional on pre-sample data and assuming Gaussian errors) is OLS.

[Nabtheberliner]

Great, thanks Tom.