Econometrics II

We have continued our occupation with introductory notions of unit root econometrics. We have concluded our preparatory work by examining the Functional Central Limit Theorem (FCLT the link concerns a special case for iid innovations), concerning the convergence in distribution to a standard Wiener process of a properly scaled partial sum process constructed by stationary, ergodic and s.m.d. (w.r.t. some filtration) innovations, and the relevant Continuous Mapping Theorem. Given this, we have finally derived the limit theory of the OLSE for a unit root AR(1)-type of process, where among others we have found super-consistency and a non-normal limiting distribution, and specified a "Dickey-Fuller type" of test for the relevant hypotheses structure of a unit root test. You can find notes on the above here.