In this paper we consider the time series dependence, stationarity, and higher moments issues of a family of first-order conditionally heteroskedastic in mean models with a possibly time-varying mean parameter. The interest in these models lies in the fact that economic theory and physics often...

A limit theory is developed for mildly explosive autoregressions under stationary (weakly or strongly dependent) conditionally heteroskedastic errors. The conditional variance process is allowed to be stationary, integrable and mixingale, thus encompassing general classes of GARCH type or...

We derive the limit theory of the Gaussian QMLE in a non-stationary Asymmetric GARCH(1,1) model when the squared innovation process lies in the domain of attraction of a stable law. When the stability parameter lies in (1,2], we find regularly varying rates and stable limits for the QMLE of the...