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\noindent Statistica Sinica {\bf 16}(2006), 213-226

\vspace{3pc} \normalsize
\centerline{\large\bf QUASI-MAXIMUM LIKELIHOOD ESTIMATION OF}
\vspace{2pt}
\centerline{\large\bf LONG-MEMORY LIMITING AGGREGATE PROCESSES}
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\author{Henghsiu Tsai}
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\centerline{\it Academia Sinica, Taipei}
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\begin{quotation}
\noindent {\it Abstract:}
We consider the application of the limiting aggregate model derived by Tsai and Chan (2005d)
for modeling aggregated long-memory data.
The model is characterized by the fractional integration order of the original process
and may be useful for
(i) modeling discrete-time data with sufficiently long sampling intervals, for example,
annual data, and/or (ii) studying the fractional integration order of the original process.
The fractional integration parameter is estimated by
maximizing the Whittle likelihood.
It is shown that the quasi-maximum likelihood estimator is asymptotically
normal, and its finite-sample properties are studied through simulation.
The efficacy of the proposed approach is demonstrated with three data analyses.\par
\vspace{9pt}
\noindent {\it Key words and phrases:}
ARFIMA models, asymptotic normality, temporal aggregation,
Whittle likelihood.\par
\end{quotation}

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