This paper investigates the asymptotic properties of the Gaussian quasi-maximum-likelihood estimators (QMLE.s) of the GARCH model augmented by including an additional explanatory variable - the so-called GARCH-X model. The additional covariate is allowed to exhibit any degree of persistence as...

Asymptotic properties of the quasi-maximum likelihood estimator (QMLE) for general ARCH(q) models - including for example Power ARCH and log-ARCH - are derived. Strong consistency is established under the assumptions that the ARCH process is geometrically ergodic, the conditional variance...

We establish sufficient conditions for the bilinear time series model to be strictly stationary and ergodic in terms of its associated Lyapunov exponent. In two special cases, we verify that the conditions are also necessary. We then use these results to give necessary and sufficient conditions...