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\footnotesize \noindent Statistica Sinica {\bf 21} (2011), 973-999

\vspace{3pc} \normalsize
\centerline{\large\bf QUASI-LIKELIHOOD
ESTIMATION IN STATIONARY AND} \vspace{2pt} \centerline{\large\bf
NONSTATIONARY AUTOREGRESSIVE MODELS} \vspace{2pt}
\centerline{\large\bf WITH RANDOM COEFFICIENTS} \vspace{.25cm}
\author{Alexander Aue and Lajos
Horv\'ath} \vspace{.4cm} \centerline{\it University of California,
Davis and University of Utah} \vspace{.55cm}
\begin{quotation}
\noindent {\it Abstract:} We propose a unified quasi-likelihood
procedure for the estimation of the unknown parameters of a
first-order random coefficient autoregressive, RCA, model that works
both for stationary and nonstationary processes. For this procedure,
the weak consistency and the asymptotic normality are established
under minimal assumptions on the noise sequences. In an empirical
study, we highlight the practicality of the quasi-likelihood
estimation for applications. As no initial knowledge about the
probabilistic properties of the RCA process is required, our
theoretical results immediately facilitate the statistical analysis
for practitioners. They may, moreover, have an impact on the
treatment of the prominent unit-root problems often encountered in
econometrics. \par
 \vspace{9pt} \noindent {\it Key words and phrases:}
Nonlinear optimization, nonlinear time series models, unit-roots.
\par
\end{quotation}
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