Structural Breakpoints in Volatility in International Markets

North America and the daily change of the 60-day interest rate concentrate 76.4 and 91.1
percent of energy at scales 1 and 2, respectively. This is depicted in Figure 1, where we
present a multi-resolution decomposition for each series. (Computations were carried out
with S+Wavelets 2.0). At each scale, the corresponding component is constructed
according to equations (7a) and (7b). Most short-term fluctuations are observed in
recomposed crystals D1 and D2, and some in the third (i.e., 8-day horizon). Meanwhile,
medium-term fluctuations are captured at the coarser scales (i.e., within 16 and 64 days).

[Figure 1]

3.2 Breakpoints in Volatility

In this section, we focus on detecting permanent shifts in volatility. We compare
wavelet analysis with Inclan and Tiao (1994)’s Iterative Cumulative Sum of Squares
(ICSS) algorithm. For the stock indices, we concentrate on two global events: the outbreak
of the Asian crisis in 1997 and the terrorist attacks of September 11, 2001. For Chile’s
interest rates, we concentrate on a domestic event triggered by a change in monetary policy
conduction in August 2001. Specifically, the sharp decrease in inflation over the last
decade—from 26 percent in 1990 to 4 percent in 2001—led the Central Bank of Chile to
switched its monetary policy interest rate from an inflation-indexed to a nominal target.

There is evidence in the literature that the ICSS algorithm tends to overestimate the
number of breakpoints, due to the fact that the assumption of independence in time-series
data is usually violated. In particular, Bacmann and Dubois (2002) point out that the
behavior of the ICSS algorithm is questionable under the presence of conditional
heteroskedasticity. They show that one way to circumvent this problem is by filtering the

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