Econometrics II

Given the use of the afore-examined CLT in order to derive conditions that ensure that the OLSE in the particular context of the stationary and ergodic AR(1) model (i.e. stationarity, ergodicity, smd property, and moment and dependence properties that ensure the convergence of particular series for the white noise process) has the usual rate and it is asymptotically normal, we were occupied with the verification of the conditions and evaluated the asymptotic variance in the context of (a stricter form of) the afore-examined conditionally heterskedastic example. This showed that the presence of conditional heteroskedasticity may affect asymptotic properties of the estimator (in this case the form of the asymptotic variance), and thereby may also affect properties of inferential procedures based on the estimator. You can find notes for the above here.

In this context we were occupied with the consideration of a feasible semi-parametric estimator for the asymptotic variance that is consistent in a stricter form of the aforementioned context involving also the existence of fourth moments. We then used it to construct a feasible and asymptotically exact and consistent Wald-type testing procedure for the AR(1) coefficient. You can find notes for the above here.