Detecting Multiple Breaks in Financial Market Volatility Dynamics

test as well as the Kokoszka and Leipus sequential sample segmentation test
(henceforth K&L and L&M, respectively).

The empirical analysis is performed using data from the stock and FX
markets. The four international stock market returns indices, the Financial
Times Stock Exchange IOO index (FTSE), the Hang-Seng Index (HSI), the
Nikkei 500 index (NIKKEI) and the Standard and Poors 500 index (S&P500)
are studied over the period 4/1/1989 - 19/10/2001 at daily frequency (sample
size, T = 3338). The data source is Datastream. The choice of the sample is
based on the recent experience of the Asian and Russian financial crises. We
also study the Yen vis-à-vis the US dollar returns over the period 1/12/1986-
30/11/1996 at 5-minute sampling frequency. The data source is Olsen and
Associates. The original sample is 1,052,064 five-minute return observations
(2653 days ∙ 288 five-minute intervals per day). The returns for some days
were removed from the sample to avoid having regular and predictable market
closures which affect the characterization of the volatility dynamics. For the
description of the data removed refer to Andersen et al. (2001). The final
sample includes 705,024 five-minute returns reflecting T = 2448 trading days.

The empirical analysis commences with investigating the hypothesis of a
single break in the four international stock market indices. The results in
Table 6 provide evidence that neither the K&L nor the I&T tests support
the null hypothesis of homogeneity in the absolute or squared returns of the
stock market indices over the sample 1989-2001. These results hold for two
alternative nonparametric estimators of (r_t)² and ∣r_t∣ used for standardizing
the maχ{⅞(fc) statistic defined in section (1.1): the VARHAC estimator and
the Nonlinear Least Squares (NLS) variance estimator of the ARMA(1,1)
for squared and absolute returns (Francq and Zakoian, 2000b). The overall
picture of the four stock market returns indices dates the change point in
1997 and in particular in the summer months of 1997 for the FTSE, HKI
and NIKKEI. The same change-point dates are also supported by the I&T
test. Using the simulation evidence in Table 2 we note that for large sample
sizes T the I&T test for ∖r_t∖ is well-behaved in terms of size and power and
is not distorted by outliers. It is interesting to note that the extension of
the I&T statistic by Kim et al. (2000) (also reported in Table 6 as B_τ(<7))
does not detect any change-points. One possible explanation can be the poor
power performance of the test in the presence of highly persistent GARCH
processes as documented in Kim et al. and as is supported by the estimation
of GARCH models for the four stock market indices (presented in the last
Table).

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