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\footnotesize \noindent Statistica Sinica {\bf 21} (2011), 1807-1829

\footnotesize \noindent doi:http://dx.doi.org/10.5705/ss.2009.090

\vspace{3pc} \normalsize \centerline{\large\bf SCORE BASED
GOODNESS-OF-FIT TESTS} \vspace{2pt} \centerline{\large\bf  FOR TIME
SERIES} \vspace{.25cm}
\author{Shiqing Ling and Howell Tong}
\vspace{.4cm} \centerline{\it Hong Kong University of Science {\rm
\&} Technology} \centerline{\it and London School of Economics and
Political Science} \vspace{.55cm} 
\begin{quotation}
\noindent {\it Abstract:} This paper studies a class of tests useful
for testing goodness of fit of a wide variety of time series models.
These tests are based on a class of empirical processes marked by
certain scores. Major advantages of these tests are that they are
easy to implement, require only weak conditions that are usually
satisfied in practical applications, the relevant critical values
are readily available without bootstrap, and are more powerful than
the Ljung-Box test, the Li-Mak test and the Koul-Stute test in all
the cases we have tried. A comparison with the Fan-Zhang test is
included. We also extend the class of tests to include score-like
statistics.\par \vspace{9pt} \noindent {\it Key words and phrases:}
Empirical process, goodness-of-fit test, nonlinear time series,
score, time series models. \par
\end{quotation}

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