of the number of change points is reported for the alternative hypotheses,
the two information criteria and two breaks. The results show that the L&M
has good power in detecting the two change points especially when the BIC
is applied to for small and gradual changes and when applied to either re-
turn transformation for large changes. In contrast, the LWZ underestimates
the number of breaks in the GARCH parameters. Generally the L&M test
has less power in detecting small and/or monotone (gradual) changes in the
GARCH parameters as opposed to large and non-monotone changes. This
is a common feature shared by the L&M and K&L tests. It is interesting to
note that in detecting changes in the distribution of the GARCH process the
absolute rather than squared returns transformation yields relatively higher
power with the BIC. Overall increasing the sample size, T, and the number of
segments, tfe, improves the power of the test especially when the size of change
is small. For large breaks the L&M and K&L share similar power. However
for small or monotone changes the K&L has relatively more power and is
computationally less demanding than the L&M test. The latter however has
better size properties and does not overpredict the number of breaks.
3 Empirical Results
There is a plethora of empirical evidence that squared asset returns exhibit
dynamic heteroskedasticity (e.g. Bollerslev et al., 1994) and absolute returns
feature long-range dependence (e.g. Granger and Ding, 1996). Empirical
studies recognize that the existence of breaks or regime changes in financial
markets affects volatility and long-range dependence in stock returns (e.g.
Lamourex and Lastrapes, 1990, Mikosch and Starica, 1999, Granger and
Hyung, 1999, Diebold and Inoue, 2001).
The empirical analysis aims to complement the simulation evidence in the
following directions. We examine the change-point hypothesis in volatility
dynamics of international stock market indices and FX returns. The empiri-
cal performance of the tests, discussed in the previous sections, is evaluated
by examining the relation of the change-points to economic events detected
not only in the squared and absolute returns but also to a family of data-
driven volatility filters. Moreover, we estimate the volatility in subsamples
prior and post breaks in an attempt to verify changes in the dependence of
the series. The empirical analysis also complements the simulation results
to tests for multiple breaks using the Lavielle and Moulines least-squares
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