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\footnotesize
\noindent Statistica Sinica {\bf 11}(2001), 273-287
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\centerline{\large\bf GEOMETRIC TRANSIENCE OF NONLINEAR TIME SERIES}
\vspace{.25cm}
\centerline{Daren B. H. Cline and Huay-min H. Pu}
\vspace{.4cm}
\centerline{{\it Texas A}\&{\it M University}}
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\begin{quotation}
\noindent {\it Abstract:}
In this paper we provide conditions for nonlinear time series to be
geometrically explosive with positive probability. The paper complements
earlier work by the authors on geometrically ergodic nonlinear time series,
showing that the conditions for examples in the earlier paper are sharp. We
also study the transience of polynomial autoregression models.\par
\vspace{9pt} \noindent {\it Key words and phrases:}
Markov chain, nonlinear time series, transience.
\end{quotation}
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