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\footnotesize \noindent Statistica Sinica {\bf 21} (2011), 779-805

\vspace{3pc} \normalsize \centerline{\large\bf LEAST ABSOLUTE
DEVIATION ESTIMATION FOR} \vspace{2pt} \centerline{\large\bf GENERAL
ARMA TIME SERIES MODELS} \vspace{2pt} \centerline{\large\bf WITH
INFINITE VARIANCE} \vspace{.25cm}
\author{Rongning Wu}
\vspace{.4cm} \centerline{\it %Baruch College and
Baruch College} \vspace{.55cm}
\begin{quotation}
\noindent {\it Abstract:} We study least absolute deviation (LAD)
estimation for general autoregressive moving average (ARMA) models
with infinite variance. The assumptions of causality and
invertibility, which are necessary for Gaussian ARMA models to
ensure the identifiability of the model parameters, are removed
because they are not required for models with non-Gaussian noise.
Following the approach taken by Davis, Knight, and Liu (1992)
 and Davis (1996),
 we derive a functional limit theorem
for random processes based on the LAD objective function, and
establish asymptotic results of the LAD estimator. A simulation
study is presented to evaluate the finite sample performance of LAD
estimation. An empirical example of financial time series is also
provided. \par \vspace{9pt} \noindent {\it Key words and phrases:}
ARMA model, infinite variance, LAD estimation, noncausality,
noninvertibility, stable distribution, time series. \par
\end{quotation}

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