Robust estimation and resampling in financial time series models

Volatility modelling has its special significance in the financial world as it is an indispensable
factor in quantifying risk, derivative pricing and so on. A reasonable model will provide accurate
forecast of volatilities and is therefore of great importance to financial market participants and policymaking
institutions. As a popular volatility model proposed by Bollerslev (1986), the generalized
autoregressive conditional heterscedasticity (GARCH) model has been studied by numbers of
researchers. Since then, some extended models have also been proposed, e.g., IGARCH, GJR,
TGARCH, and these models have enriched the prediction of volatility.
AIM: A commonly used method for estimating the unknown parameters in GARCH-type models
is quasi maximum likelihood estimation (QMLE), in which the errors are assumed to follow normal
distribution. However, studies have shown that heavy tails exist in error distributions for most of the
financial time series that we come across in practice which makes QMLE an inappropriate approach.
Therefore, there is a great need for developing more robust methods which work for heavy-tailed
distribution and this is what I will investigate my PhD research.
Specifically, let { } t X (t Z ) denote a series of observations for financial time series and
consider a general model that