Econometrics II

We have been occupied with further issues concerning the GARCH(1,1)processes, as for example that they cannot simultaneously have symmetric marginal distribution and exhibit phenomena of negative dynamic asymmetry (under the relevant moment existence assumptions), their extension to finite and arbitrary orders and the plausibility of the semi-parametric Gaussian QMLE in their context.

We have been occupied with the examination of the limit theory of the OLSE for the autoregressive parameter for an appropriate form of an AR(1)-ARCH(1) process. You can find notes for this here and compare our derivations with the analogous ones we have derived in previous lectures, for an AR(1) process with a different form of conditional hereoskedasticity (see for example here and here). We have essentially seen that the asymptotic variance estimator and the subsequent Wald-type testing procedure have robust properties under both forms of conditional heteroskedasticity.

We have finally been occupied with another example of a conditionally heteroskedastic model, namely the EGARCH(1,1) one. We derived the properties required from our general definition of conditional heteroskedasticity (partially in the restricted context of conditional standard normality and of zero "magnitude" parameter), and established the model's comparative-to the GARCH case-flexibility w.r.t parameter restrictions for the establishment of suchlike properties as well as w.r.t. to the reproduction of the relevant financial returns stylized facts (in the aforementioned restricted context). You can find notes for the above here (as well as some similar derivations in a more general context here and here).