Publication: The change-point problem and segmentation of processes with conditional heteroskedasticity
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2013-06
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Abstract
In this paper we explore, analyse and apply the change-points detection and location procedures
to conditional heteroskedastic processes. We focus on processes that have constant conditional
mean, but present a dynamic behavior in the conditional variance and which can also be affected
by structural changes. Thus, the goal is to explore, analyse and apply the change-point detection
and estimation methods to the situation when the conditional variance of a univariate process is
heteroskedastic and exhibits change-points. Based on the fact that a GARCH process can be
expressed as an ARMA model in the squares of the variable, we propose to detect and locate
change-points by using the Bayesian Information Criterion as an extension of its application in
linear models. The proposed procedure is characterized by its computational simplicity,
reducing difficulties of the change-point detection in the complex non-linear processes.
We compare this procedure with others available in the literature, which are based on cusum
methods (Inclán and Tiao (1994), Kokoszka and Leipus (1999), Lee et al. (2004)), informational
approach (Fukuda, 2010), minimum description length principle (Davis and Rodriguez-Yam
(2008)), and the time varying spectrum (Ombao et al (2002)). We compute the empirical size
and power properties by Monte Carlo simulation experiments considering several scenarios. We
obtained a good size and power properties in detecting even small magnitudes of change and for
low levels of persistence.
The procedures were applied to the S\&P500 log returns time series, in order to compare with
the results in Andreou and Ghysels (2002) and Davis and Rodriguez-Yam (2008). Changepoints
detected by the proposed procedure were similar to the breaks found by the other
procedures, and their location can be related with the Southeast Asia financial crisis and with
other known financial events.
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Keywords
Heteroskedastic time series, Segmentation, Change-points