Econometrics II

Using the Birkhoff's LLN and the CMT we have derived the strong consistency of the OLSE in the context of a stationary and ergodic AR(1) process. Moving on to the issue of establishing a CLT for stationary and dependent processes, we have examined the notions of the filtration, adaptation to a filtration, of a martingale difference process w.r.t. a filtration, and of a square integrable martingale difference process w.r.t. a filtration. We begun the construction and the examination of a strictly stationary, ergodic and square integrable martingale different process that in some cases it is also appropriately conditionally heteroskedastic.