Econometrics II

We have been occupied with the definition of the GARCH(1,1) process, the existence and uniqueness of a stationary and ergodic solution to the relevant stochastic recurrence equation, the issue of the weak stationarity of the solution, and the issue of the ARMA(1,1) representation of the squared process under the appropriate restrictions. We thus obtained a non-linear process for which the properties of strict stationarity and ergodicity stem from weaker conditions compared to them that imply weak stationarity. Under stricter conditions we obtain a process that in addition to being an appropriate stationary and ergodic smd process, its squares constitute an ARMA(1,1) w.r.t. a relevant s.m.d. process. This is in partial accordance to some of the stylized facts of financial asset returns in some observation frequencies. You can find notes on this issue here.