MLE for change-point in ARMA-GARCH models with a changing drift

This paper investigates the maximum likelihood estimator (MLE) of structure-changed ARMA-GARCH models. The convergent rates of the estimated change-point and other estimated parameters axe obtained. After suitably normalized, it is shown that the estimated change-point has the same asymptotic distribution as that in Picard(1985) and Yao(1987). Other estimated parameters are shown to be asymptotically normal. As special cases, we obtain the asymptotic distributions of MLEs for structure-changed GARCH models, structure-changed ARMA models with structure-unchanged GARCH errors, and structure-changed ARMA models with i.i.d. errors, respectively