The main goal when fitting GARCH models to conditionally heteroscedastic time series is to estimate the underlying volatilities. It is well known that outliers affect the estimation of the GARCH parameters. However, little is known about their effects when estimating volatilities. In this paper,...

Changes in variance or volatility over time can be modelled using stochastic volatility (SV) models. This approach is based on treating the variance as an unobservable variable, the logarithm of which is modelled as a linear stochastic process, usually an autoregression. Although it is not easy...

GARCH volatilities depend on the unconditional variance, which is a non-linear function of the parameters. Consequently, they can have larger biases than estimated parameters. Using robust methods to estimate both parameters and volatilities is shown to outperform Maximum Likelihood procedures.

This paper studies the nonlinear dependences in daily returns of 40 French stocks and two indices, the Vontobel-Datastream index and the official French index CAC40. These returns are studied during a period of twenty-four years beginning January 1, 1975. The rescaled range analysis of Hurst and...