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 a limit theorem for appropriately centered and scaled martingale transforms of the form sum_{i=1}^{n}\xi_{i}V_{i} to mixed-stable limits when (\xi_{i})_{i\in\mathbb{Z}} is an iid sequence in the domain of attraction of an alpha-stable distribution where alpha\in(0,2]. Using the...

We derive a limit theorem for appropriately centered and scaled martingale transforms \sum_{i=1}^{n}\xi_{i}V_{i} to mixed-stable limits when \left(\xi_{i}\right) is an iid sequence in the domain of attraction of an \alpha-stable distribution where \alpha\in(0,2]. Using the Principle of...