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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。
In order to study the movement patterns of Shanghai-Shenzhen 300 Index Stochastic Process, capture the three characteristics of non-Gaussian interest, volatility accumulation and leverage effect of financial assets. Based on the time series analysis, we construct four different The discrete time-varying volatility Levy process, and established the state space model of volatility, drift rate and jump, and introduced the particle filter method to study the dynamic volatility and jump type. The results show that there are a large number of random jumps in the CSI 300 Index, while Brownian motion can not characterize these jumps, and the Kalman filter can not track the jump state correctly. However, the time-varying activity level of the assets under the harmonic steady- And jumping morphology has the best capture capabilities.