Structural Breakpoints in Volatility in International Markets

(2003) apply wavelet analysis to estimate the systematic risk of an asset (beta). Lee (2001a)
studies the interaction between the U.S. and the South Korean stock markets. He finds
evidence of price and volatility spillover effects from the U.S. stock market to the Korean
stock market, but not vice versa. In turn Lee (2001b) illustrates the use of wavelets for
seasonality filtering of time-series data.

This paper is organized as follows. Section II gives a brief background on wavelet
analysis. Section III focuses on detection of breakpoints in volatility by the ICSS algorithm
and wavelet methods for a sample of four stock indices (Emerging Asia, Europe, Latin
America, and North America), and interest rates series paid on deposits by Chilean banks
(nominal and inflation-indexed). We test for variance homogeneity in the original series,
and in the series filtered out for both conditional heteroskedasticity and serial correlation.
Section IV presents our main conclusions.

The contribution of this article is twofold. First, it provides new evidence that
reinforces the importance of controlling for both conditional heteroskedasticity and serial
correlation prior to testing for variance homogeneity. Second, it makes a parallel between
the ICSS algorithm and wavelet analysis, showing that the latter tends to be more robust.
To our knowledge, no one has yet conducted a similar study.

II Wavelet Analysis in a Nutshell

Wavelets or short waves are similar to sine and cosine functions in that they also
oscillates about zero. However, as its name indicates, oscillations of a wavelet fade away
around zero, and the function is localized in time or space.¹ In wavelet analysis, a signal
(i.e., a sequence of numerical measurements) is represented as a linear combination of
wavelet functions.

¹ Mathematically, a function w(.) defined over the entire real axis is called a wavelet if w(t)→0 as t→±∞.

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