基于自举粒子滤波的沪深300指数跳跃性形态

Application of Bootstrap Particle Filtering for Jumps:Evidence from H&S 300 Index

为研究沪深300指数价格随机过程的运动形态,捕捉金融资产的非高斯新息、波动率集聚和杠杆效应三大特征,在时间序列分析的基础上,采用非对称GARCH模型构建了四种不同跳跃程度的离散时变波动率Levy过程,并建立了波动率、漂移率和跳跃的状态空间模型,同时引入粒子滤波方法来研究动态波动率和跳跃类型。研究表明:沪深300指数收益率存在大量的随机跳跃,而布朗运动无法刻画这些跳跃,且卡尔曼滤波也无法正确追踪跳跃状态,而调和稳态过程下粒子滤波对资产的时变活动率水平和跳跃形态上具有最佳的捕获能力。

This paper models four kinds of Levy processes with discrete time-varying volatility according to different degrees of jump, applying asymmetric GARCH model based on time series analysis, to capture non-Gaussian innovations, volatility clustering and leverage effects of H＆S 300 Index. Furthermore, it builds three-dimensional state space model of volatility, drift rate and jump and introduces particle filtering method to analyze dynamic volatility process and jumps. The empirical results show that there exists a large number of stochastic jumps in returns of H＆S 300 Index, and that neither Brownian motion nor Kalman filter can capture those jumps. However, particle filter with tempered stable process displays optimal fitting in describing time-varying activity and jumps of assets.