О практической применимости трех CUSUM-методов к обнаружению структурных сдвигов в EGARCH-моделях

Вестник Санкт-Петербургского университета. Серия 10. Прикладная математика. Информатика. Процессы управления. 2020. Т. 16. № 1. С. 19–30.

Borzykh D., Yazykov A.

There are three well-known CUSUM-methods of structural breaks detection for standard
GARCH-models in the literature: (Inclґan, Tiao, 1994), (Kokoszka, Leipus, 1999) and (Lee,
Tokutsu, Maekawa, 2004). Despite the fact that these algorithms were initially developed
for standard GARCH-models, there are theoretical arguments that CUSUM-methods can
be applied to EGARCH-models. What is more, one can find empirical research which uses
these methods to detect structural breaks in real-time series volatility. However, we have not
found any numeric experiments which would prove the applicability of CUSUM-methods
for EGARCH models so far. We are not aware of any controlled experiments conducted in
order to verify the applicability of these methods for EGARCH models. This article adds to
the existing literature in the following way. We first generate volatility series which possess
EGARCH-model with known structural breaks. Then we run simulations and show that
CUSUM-methods are weak in detecting structural breaks on medium size samples which
are close to real ones. We conclude that the applicability of these methods on EGARCH
models is limited. Therefore, we suggest a hybrid algorithm which is able to improve the
performance of CUSUM-methods when detecting structural breaks in all EGARCH-models.

Keywords: волатильность, структурные сдвиги, volatility, EGARCH, structural breaks, CUSUM, CUSUM, change points, EGARCH