Robust estimation and resampling in financial time series models

波动率建模在金融领域有着特殊的意义，它是量化风险、衍生品定价等方面不可缺少的因素，合理的波动率模型能够准确地预测波动率，对金融市场参与者和决策机构具有重要意义。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，受到了众多学者的研究。从那时起，也提出了一些扩展模型，例如，IGARCH、GJR、TGARCH等模型丰富了波动率的预测。目的：在GARCH类模型中，估计未知参数的一种常用方法是拟极大似然估计（QMLE），它假定误差服从正态分布。然而，研究表明，重尾存在于我们在实践中遇到的大多数金融时间序列的误差分布中，这使得QMLE是一种不合适的方法。因此，非常需要开发适用于重尾分布的更强大的方法，这就是我将研究的博士研究。具体来说，令{ } t X（t Z）表示金融时间序列一系列观测值，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