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\noindent Statistica Sinica {\bf 15}(2005), 795-817

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\centerline{\large\bf MODEL DIAGNOSIS FOR SETAR TIME SERIES}
\vspace{.25cm}
\author{Hira L. Koul$^1$, Winfried Stute$^2$ and Fang Li$^1$}
\vspace{.4cm}
\centerline{\it $^1$Michigan State University and $^2$University of Giessen}
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\begin{quotation}
\noindent {\it Abstract:}
This paper discusses asymptotically distribution free (ADF) tests
in self-exciting threshold autoregressive (SETAR) models.
We also consider the case when the two different
line segments have no jump. These tests are based on a
marked empirical process of the underlying residuals. The paper
also discusses the asymptotic behavior of the residual empirical process
and ADF tests for the
error distribution. We find that under some mild conditions,
the asymptotic null behavior of both of these processes does not
depend on the preliminary estimator of the change point parameter.
Moreover, somewhat surprisingly, the asymptotic behavior
of the residual empirical process in these models is the same as in the
one-sample location model, as long as the residuals are based on an
asymptotically linear estimator of the line segment parameters.
The paper also includes a simulation study analyzing the finite
sample behavior of some of the proposed tests.\par
\vspace{9pt}
\noindent {\it Key words and phrases:}
Marked point processes, martingale type transform, model checks, time series.\par
\end{quotation}
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