Remarks on stationary GARCH processes under heavy tail distributions

Marc Taberner-Ortiz, Manfred Denker

Let $(X_n{)}_{n\in \mathbb{Z}}$ be a GARCH process with $E(X_0^4)<\infty$, and let ${\mu }_n$ denote the distribution of $\frac{1}{\sqrt{n}}{\sum }_{i=1}^n[X_i^2-\mathbb{E}(X_0^2)]$. We derive…