Structural Breakpoints in Volatility in International Markets

return series by a GARCH (1,1) model, and applying the ICSS algorithm to the
standardized residuals. By applying this procedure (and an alternative one they propose) to
stock market indexes in ten emerging markets, Bacmann and Dubois obtain results that
differ to great extent from those in Aggarwal, Inclan and Leal (1999). They conclude that
structural breaks in unconditional variance are less frequent than it was shown previously.

Based on this evidence, we test for volatility shifts before and after filtering the data
for conditional heteroskedascity and serial correlation. As shown below, the number of
shifts detected by the ICSS algorithm and wavelets methods is substantially reduced when
the data is filtered.

The next two sections briefly describe the wavelet variance analysis and the ICSS
algorithm.

3.2.1 Wavelet Variance Analysis

Wavelet variance analysis consists in partitioning the variance of a time series into
pieces that are associated to different time scales. It tells us what scales are important
contributors to the overall variability of a series (see Percival and Walden, 2000). In
particular, let x1, x2,..., xn be a time series of interest, which is assumed to be a realization of
a stationary process with variance σ²_X . If υ²_X (τ_j ) denotes the wavelet variance for scale
τj≡2^j-1, then the following relationship holds:

∞

σ²_X = ∑υ²_x(τ_j)                                                           (9)

j=1

This relationship is analogous to that between the variance of a stationary process and its
spectral density function (SDF):

1/2

σ²X = ∫SX(f)df                                                       (10)

-1 / 2

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