Detecting Multiple Breaks in Financial Market Volatility Dynamics

4 Conclusions

There is a substantial literature on testing for the presence of breaks in lin-
early dependent stochastic processes. The purpose of this paper is to explore
recent advances in the theory of change-point estimation, using various new
CUSUM type change-point estimators and tests for multiple breaks in the
context of volatility models. The tests are not model-specific and apply to
a large class of strongly dependent processes such as ARCH and SV type
processes and were developed in a series of recent papers in particular by
Kokoszka and Leipus (1998, 1999, 2000) and Lavielle and Moulines (2000).
We focus on the Kokoszka and Leipus (2000) and Lavielle and Moulines
(2000) tests which monitor nonlinear transformations of returns processes
(in square and absolute returns) without the need to specify any particu-
lar, restrictive functional form of the process. Moreover, the CUSUM type
test of Kokoszka and Leipus and the RSS minimization type test of Lavielle
and Moulines are characterized by relative computational simplicity which
is an additional advantage for the complex nonlinear structure of financial
time series. So far only limited simulation and empirical evidence is reported
about these tests. We enlarge the scope of applicability by suggesting sev-
eral improvements that enhance the practical implementation of the proposed
tests. The extensive simulation investigation regarding the performance of
the Kokoszka and Leipus test provides evidence that the test has good power
properties in detecting even small changes in all the GARCH parameters and
the error and appears robust to outliers, but suffers some size distortions in
the persistent GARCH case.¹² For the multiple breaks hypothesis we find
that both tests share good power properties especially the BIC criterion in
the RSS of Lavielle and Moulines. We also suggest the application of these
change-point tests to more precise measures of volatility, including the high
frequency data-driven processes studied by Andersen et al. (2001), Andreou
and Ghysels (2000), Barndorff-Nielsen and Shephard (2000), among others.

The empirical analysis examines various financial series, including equity
index returns for several financial markets in the Hong Kong, Japan, the
U.K. and U.S. The data series are similar to several prior studies, particularly
Granger and Hyung (1999) who consider a longer but less recent sample. The
applications of the Kokoszka and Leipus as well as the Lavielle and Moulines

¹²The IGARCH type of models violate the assumption of finite fourth moments required
by the Kokoszka and Leipus tests.

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