In this thesis, we proposed a minimum Hellinger distance estimator (MHDE) and a minimum profile Hellinger distance estimator (MPHDE) for estimating the parameters in the ARCH and GARCH models depending on whether the innovation distribution is specified or not. The asymptotic properties of MHDE and MPHDE were examined through graphs as the theoretical investigation of them are more involved and needs further study in the future research. Moreover, we demonstrated the finite-sample performance

more »

... both MHDE and MPHDE through simulation studies and compared them with the well-established methods including maximum likelihood estimation (MLE), Gaussian Quasi-MLE (GQMLE) and Non-Gaussian Quasi-MLE (NGQMLE). Our numerical results showed that MHDE and MPHDE have better performance in terms of bias, MSE and coverage probability (CP) when the data are contaminated, which testified to the robustness of MHD-type estimators.