polynomial augmented generalized autoregressive conditional heteroscedasticity models (GARCH) is proven. The result extend the … results of (Berkes et al., 2003) and (Francq and Zakoïan, 2004) of the standard GARCH model to augmented GARCH models … introduced by (Duan, 1997) which contains many commonly employed GARCH models as special cases. The conditions for consistency …