Assessing the bias of maximum likelihood estimates of contaminated garch models

It is well known that Gaussian maximum likelihood estimates of time series models are not robust. In this paper we prove this is also the case for the Generalized Autoregressive Conditional Heteroscedastic (GARCH) models. By expressing the Gaussian maximum likelihood estimates as Ψ estimates and by assuming the existence of a contaminated process, we prove they possess zero breakdown point and unbounded influence curves. By simulating GARCH processes under several proportions of contaminations we assess how much biased the maximum likelihood estimates may become and compare these results to a robust alternative. The t-student maximum likelihood estimates of GARCH models are also considered.