The change-points detected in the three international stock market indices
in Table 6 refer to the Asian crisis period. However the single change point
hypothesis can mask the existence of multiple breaks which implies that in
dating change-points it is advisable to follow a multiple breaks procedure.
The results of two tests are summarized in Table 7. In the Lavielle and
Moulines test we adopt two penalty function criteria, the first is the Bayesian
Information Set (BIC) and the second is a modified BIC as proposed in Liu et
al. (1996) (denoted by LWZ in Table 7) and we set the number of segments
⅛ equal to 3 and 5. The empirical findings show that irrespective of the
choice of ⅛ the L&M test consistently detects the same number of breaks.
Specifically the combination of the BIC and ∖rt∖ tends to predict the largest
number of breaks whereas the pair of LWZ and (rt)2 the smallest number of
change-points. The latter result is consistent with the conservatism of the
LWZ found in the simulation analysis. The Asian crisis period appears to
be a common break in the above combinations (of processes and information
criteria) and in all stock market indices that is revealed in different months of
1997. In July and August 1997 we detect the first change-points associated
with the Asian crisis in the FTSE, HSI and NIKKEI followed by the October
1997 change-point in the S&P500 as well as the NIKKEI.11 A second common
break in the stock indices that is revealed in the L&M procedure is associated
with the Russian crisis. In July 1998 we detect change-points in the FTSE
and the S&P500 followed by the August 1998 break in the NIKKEI. Table
8 reports the results of multiple breaks from the Kokoszka and Leipus test
sequential application. Comparing the results from the two tests we observe
that the latter test detects a larger number of breaks especially when applied
to the ∖rt∖ process even at the 1% significance level. The two multiple change-
point tests detect some common breaks in the same year mainly that of 1997.
As a final empirical application we test for change-points in the FX market
applying the K&L test to the family of high-frequency volatility filters that
estimate the Quadratic Variation (QV) of diffusion processes with stochastic
volatility (briefly discussed in section 1.3). These high-frequency volatility
estimates have been introduced by Merton (1980) and applied in Poterba
and Summers (1986), French et al. (1987) and Hsieh (1991) interalia. More
recently Andersen and Bollerslev (1998) reintroduced these filters using in-
11A detailed chronology of the Asian financial crisis events
in 1997 and 1998 produced by N. Roubini can be found at
http://www.stern.nyu.edu/nroubini/asia/AsiaChronologyl.hml.
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