Econometrics II

We were occupied further with issues concerning statistical inference in ARMA models in the framework of correct statistical specification and of known unit variance for the white noise process. We pointed out that in the context of general AR models the extraction of the asymptotic properties of the OLSE can be similar to the one we have taken in the case of the AR(1) model modulo technical details of essentially multivariate nature that are not present in the latter case. We have studied issues concerning the semi-parametric estimation of such models introducing the Gaussian Quasi Maximum Likelihood Estimator (Gaussian QMLE), in cases where the MA component is non trivial (exe: show that the Gaussian QMLE coincides with the OLSE when the MA component is trivial, the orders of the MA and AR components are known and this information is used). We also abstractly discussed the numerical nature of its derivation, and were briefly and not rigorously occupied with its strong consistency under the relevant assumption framework concerning the MA(1) model. You can find notes on the above here.