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\footnotesize
\noindent Statistica Sinica {\bf 16}(2006), 15-28

\vspace{3pc} \normalsize
\centerline{\large\bf QUANTILE INFERENCE FOR NEAR-INTEGRATED}
\vspace{2pt}
\centerline{\large\bf AUTOREGRESSIVE TIME SERIES}
\vspace{2pt}
\centerline{\large\bf WITH INFINITE VARIANCE}
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\author{Ngai Hang Chan, Liang Peng and Yongcheng Qi}
\vspace{.4cm}
\centerline{\it The Chinese University of Hong Kong, Georgia Institute of Technology}
\centerline{\it and University of Minnesota Duluth}
\vspace{.55cm}

\begin{quotation}
\noindent {\it Abstract:}
The
limiting distribution of the quantile estimate for the autoregressive
coefficient of a near-integrated
first order autoregressive model with infinite variance errors
is derived.  Since the limiting distribution depends on the
unknown density function of the errors, an empirical
likelihood ratio statistic is proposed from which
confidence intervals can be constructed for the near unit root model
without knowing the density function.
Numerical simulations are conducted to compare the performance of
the empirical likelihood method and the least squares procedure.  It
is found that  the empirical likelihood method outperforms
the least squares procedure in general.\par
\vspace{9pt}
\noindent {\it Key words and phrases:}
Empirical likelihood method, infinite variance,
near unit root, quantile estimate.\par
\end{quotation}

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