The Maximum likelihood estimation (MLE) is the most widely used method to estimate the parameters of a GARCH(p,q) process. This is owed to the fact that the MLE, among other properties, is asymptotically efficient. Even though the MLE is sensitive to outliers, which can occur in time series. In...

In parametric time series analysis there is the implicit assumption of no aberrant observations, so-called outliers. Outliers are observations that seem to be inconsistent with the assumed model. When these observations are included to estimate the model parameters, the resulting estimates are...

Nonparametric prediction of time series is a viable alternative to parametric prediction, since parametric prediction relies on the correct specification of the process, its order and the distribution of the innovations. Often these are not known and have to be estimated from the data. Another...

The ARCH model introduced by Engle [1982] and extended to the GARCH model byBollerslev [1986] is able to capture some of the stylized facts of nancial data Rama [2001].The analysis of nancial time series is sensitive to outliers, due to the temporal dependencein the data. According to Carnero et...