dent ARCH and SV type specifications given appropriate stationarity condi-
tions. The theoretical developments are described in a series of recent papers,
see in particular Kokoszka and Leipus (1998, 1999, 2000) and Lavielle and
Moulines (2000). So far only limited simulation and empirical evidence is
reported about these tests. We enlarge the scope of applicability by suggest-
ing several improvements that enhance the practical implementation of the
proposed tests. This paper focuses on the Kokoszka and Leipus (2000) and
Lavielle and Moulines (2000) tests and proposes three types of extensions.
First, we find via simulations that the VARHAC estimator proposed by den
Haan and Levin (1997) yields good properties for the CUSUM-type estima-
tor of Kokoszka and Leipus (2000). Simulation evidence is also presented for
the application of this test to the multiple breaks setting using a sequential
sample segmentation approach similar to that of Inclan and Tiao (1994).
Second, the series used in the tests so far are either squared or absolute re-
turns. We suggest the application of these tests to more precise measures
of volatility, including the high frequency data-driven processes studied by
Andersen et al. (2001), Andreou and Ghysels (2002), Barndorff-Nielsen and
Shephard (2000), among others. Third, the finite sample performance of
these new tests is assessed via extensive Monte Carlo simulations for realistic
univariate GARCH models, single and multiple breaks as well as different
algorithms and information criteria for the multiple breaks case.
The empirical application examines various financial series, including eq-
uity index returns for several financial markets in the Hong Kong, Japan,
the U.K. and U.S. as well as FX market series. Our empirical analysis is
particularly complementary to Granger and Hyung (1999) who use the tests
proposed by Inclan and Tiao (1994) and Bai (1997) to examine breaks in
the absolute returns. The advantage of the Kokoszka and Leipus as well as
Lavielle and Moulines tests is their validity under a wide class of strongly
dependent processes, including long memory, GARCH-type and nonlinear
models. The Inclan and Tiao test applies in principle to independent series
and is designed to find a break in the (unconditional) variance with unknown
location. We show via Monte Carlo that the Inclan and Tiao test has nev-
ertheless power and only minor size distortions when applied to strongly
dependent data, though it is not as powerful as the Kokoszka and Leipus
and Lavielle and Moulines tests.
The paper is organized as follows. In section 2 we describe the various
tests. Section 3 presents the Monte Carlo design and results. Section 4
contains the empirical application and a final section concludes.