Monitoring parameter change for time series models with conditional heteroscedasticity

•We consider the sequential monitoring method based on the CUSUM of score functions.•Our findings in the simulation study support the validity of our monitoring method.•The proposed method is recommendable particularly when one aims to detect a change for one specific parameter in GARCH-type models.

This paper studies the monitoring procedure to detect a parameter change in GARCH-type models based on the cumulative sum (CUSUM) of score functions as in Gombay and Serban (2009). For illustration, a simulation study is carried out for asymmetric GARCH models.