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\footnotesize \noindent Statistica Sinica {\bf 21} (2011), 1191-1200

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\centerline{\large\bf TAIL BEHAVIOR AND OLS ESTIMATION} \vspace{2pt}
\centerline{\large\bf   IN AR-GARCH MODELS} \vspace{.25cm}
\author{Theis Lange}
\vspace{.4cm} \centerline{\it University of Copenhagen}
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\begin{quotation}
\noindent {\it Abstract:}
 The scope of this paper is twofold. We
first describe the tail behavior for general AR-GARCH processes and
hence extend the results of Basrak, Davis, and Mikosch (2002b) to
another empirical relevant model class. Second, and primarily, we
study properties for the OLS estimator in general AR-GARCH model.
Specifically it is shown that the OLS estimator of the
autoregressive parameter in the AR-GARCH model has a non-standard
limiting distribution with a non-standard rate of convergence when
the innovations have non-finite fourth order moment.\par
\vspace{9pt} \noindent {\it Key words and phrases:} ARMA-GARCH,
heavy tails,  tail behavior. \par
\end{quotation}
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