On the Cusum test for parameter changes in garch(1,1) Models

By Soohwa Kim, Sinsup Cho, Sangyeol Lee. 2000

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The Cusum Test for Parameter Change in Time Series Models (2003, background): “…the time series context as economic time series often exhibit prominent evidence for structural change in the underlying model; see, for example, Wichern et al. (1976), Picard (1985), Krämer et al. (1988), Tang & MacNeil (1993), Kim et al. (2000), Lee & Park (2001), and the papers cited therein.”
High moment partial sum processes of residuals in GARCH models and their applications (2005, unknown): “In addition, we include the near integrated GARCH cases with α1 = 0.1 or 0.167 and β1 = 0.8 or 0.867 that were shown to have poor performance in Kim, Cho and Lee’s test [17].”
The Cusum Test for Parameter Change in Regression Models with ARCH Errors (2004, methodology): “The proof was of an independent interest since the mixingale approach adopted by Kim et al. (2000) is not easy to apply, and the proof would be much lengthier without the beta mixing condition.”
Detecting multiple breaks in financial market volatility dynamics (2002, methodology): “It is interesting to note that the extension of the I&T statistic by Kim et al. (2000) (also reported in Table 6 as BT (C)) does not detect any change-points.”