Robust estimation and resampling in financial time series models

波动率模型在金融领域有着特殊的意义，因为它是量化风险、衍生品定价等不可缺少的因素。一个合理的模型将提供准确的波动预测，因此对金融市场参与者和政策制定机构具有重要意义。广义自回归条件异方差（GARCH）模型作为Bollerslev（1986）提出的一种流行的波动率模型，已经得到了许多研究者的研究。此后，一些扩展模型也被提出，如IGARCH、GJR、TGARCH，这些模型丰富了波动率的预测。目的：garch模型中常用的未知参数估计方法是拟极大似然估计（quasi maximum likelihood estimation， QMLE），该方法假定误差服从正态分布。然而，研究表明，在我们在实践中遇到的大多数金融时间序列的误差分布中存在重尾，这使得QMLE成为不合适的方法。因此，非常需要开发更强大的方法，用于重尾分布，这是我将调查我的博士研究。具体来说，让{}t X （t Z）表示金融时间序列的一系列观测值，并考虑一个一般模型

Volatility modelling has its special significance in the financial world as it is an indispensablefactor in quantifying risk, derivative pricing and so on. A reasonable model will provide accurateforecast of volatilities and is therefore of great importance to financial market participants and policymakinginstitutions. As a popular volatility model proposed by Bollerslev (1986), the generalizedautoregressive conditional heterscedasticity (GARCH) model has been studied by numbers ofresearchers. 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 modelsis quasi maximum likelihood estimation (QMLE), in which the errors are assumed to follow normaldistribution. However, studies have shown that heavy tails exist in error distributions for most of thefinancial 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-taileddistribution 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 andconsider a general model that