Robust estimation and resampling in financial time series models

波动率模型在金融领域具有特殊的意义，因为它是量化风险、衍生品定价等不可或缺的因素。一个合理的模型将提供对波动性的准确预测，因此对金融市场参与者和政策制定机构具有重要意义。作为Bollerslev(1986)提出的一种流行的波动率模型，广义自回归条件异方差(GARCH)模型已被众多研究者所研究。此后，又提出了IGARCH、GJR、TGARCH等扩展模型，丰富了对波动性的预测。目的：在GARCH型模型中，一种常用的估计未知参数的方法是拟极大似然估计(QMLE)，该方法假设误差服从正态分布。然而，研究表明，我们在实际中遇到的大多数金融时间序列的误差分布都存在重尾，这使得QMLE不适合用于处理重尾分布。因此，非常需要开发更健壮的方法来处理重尾分布，这也是我将进行的博士研究。具体地说，设{}t X(T Z)表示金融时间序列的一系列观测，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