Abstract
We consider a linear regression model with errors modelled by marginale difference sequences, which include heteroskedastic augmented GARCH processes. We develop asymptotic theory for two monitoring schemes aimed at detecting a change in the regression parameters.
The first method is based on the CUSUM of the residuals and was studied earlier in the context of independent identically distributed errors. The second method in new and is based on the square of prediction errors.
Both methods have correct asymptotic size and detect a change with probability approaching unity. They are illustrated and compared in a small simulation study.