Detecting Multiple Breaks in Financial Market Volatility Dynamics

ternative hypothesis of multiple change points the process (2.2) is simulated
with different sources of breaks as described under Hf, Hf, Hf Hf above.
In order to detect the two breaks at 0.33 ("7iT) and 0.66 of the sample (2τιT)
we first apply the Kokoszka and Leipus (2000) test to the total sample (T) of
X_t and if a break is detected an algorithm similar to that of Inclan and Tiao
(1994) is applied according to which the sample is segmented and the test
is applied again to each subsample following sequential sample segmentation
whenever a break is detected. The simulation design sequentially applies
the test for upto 5 segments. Hence a 1% significance level is applied to
each segment. The Lavielle and Moulines (2000) test is also applied to the
multiple breaks process (as well as single break case mainly for comparison
purposes with the K&L and I&T tests). This test simultaneously detects the
number of change points and dates the breaks. The Lavielle and Moulines
is a least squares type test and in order to detect multiple breaks one may
apply a grid search approach or a more efficient algorithm based on dynamic
programming suggested in Bellman and Roth (1969) and reintroduced in Bai
and Perron (1998, 2002). Two information criteria are used for the penalty
function: the BIC (Bayesian Information Criterion) and its modification by
Liu et al. (1997) denoted LWZ. The simulation as well as empirical analysis
is performed using the GAUSS programing language.

The simulation investigation is organized as follows: First, we consider
the application of the I&T, K&L and L&M tests in model (2.1) to evaluate
their size and power under the single break hypothesis. The alternative
hypotheses aim to examine the power of the test in detecting breaks due
to either changes in the parameters (defined by Hf, Hf) or the error of
the GARCH process (defined by Hf ,Hf). The former are interesting for
studying the parameter constancy of the GARCH dynamics whereas the
latter for examining the distributional homogeneity of the process. Both are
the underlying assumptions in many asset pricing relationships and Value
at Risk (VaR). Second, we evaluate the performance of the K&L and L&M
tests for multiple breaks for the alternative hypotheses mentioned above.

2.2 Simulation Results

The simulation results commence with the evaluation of the K&L test when
the underlying process is a Normal-GARCH(I₅I). Table 1 reports only minor
size distortions for GARCH models with low persistence (e.g. DGPl where
^ao + β₀ ⁼ 0.6). These minor distortions remain as the sample size increases

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