On the practical applicability of three CUSUM-methods for structural breaks detection in EGARCH-models

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.