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SVR-ARMA-GARCH models provide flexible model fitting and good predictive powers for nonlinear heteroscedastic time series datasets. In this study, we explore the change point detection problem in the SVR-ARMA-GARCH model using the residual-based CUSUM test. For this task, we propose an alternating recursive estimation (ARE) method to improve the estimation accuracy of residuals. Moreover, we suggest using a new testing method with a time-varying control limit that significantly improves the detection power of the CUSUM test. Our numerical analysis exhibits the merits of the proposed methods in SVR-ARMA-GARCH models. A real data example is also conducted using BDI data for illustration, which also confirms the validity of our methods.