周期性异质波动SV模型的Bayesian估计  

Bayesian Estimation of SV Model with Periodic Heterogenous Volatility

作　　者：张海燕 高鑫杰 于玲玉 ZHANG Hai-yan;GAO Xin-jie;YU Ling-yu(School of mathematics and statistics,Changchun University of Technology,Changchun 130012,China)

机构地区：[1]长春工业大学数学与统计学院,吉林长春130012

出　　处：《数理统计与管理》2021年第6期1031-1050,共20页Journal of Applied Statistics and Management

基　　金：教育部人文社会科学研究资助项目(12YJA790187);吉林省科技发展计划项目软科学资助项目(20140418053FG);吉林省教育厅“十二五”社会科学研究资助项目(吉教科文合字[2014]第57号).

摘　　要：本文从描述时间序列波动聚类性质的SV模型出发,以金融应用为背景设定均值方程具有厚尾T分布.针对金融数据中常见的周期性异质现象,设定描述乘性异质波动的SV模型,并以周期性波动成分作为混合参数将之表示为正态分布尺度混合(SMN)形式,推导了模型的Bayesian后验分级模型,由此估计SV模型的参数.混合参数的先验分布尝试两种设定,一是参考以往SMN应用文献设定为IGamma(v/2,v/2)分布,二是结合实际应用背景区别于以往文献提出一种适应性先验.模拟结果说明两种先验均可获得准确的参数估计,并准确提取周期性异质波动成分,而适应性先验具有更高的估计精度,且在波动分析方面表现出显著优势.在沪深两市的实证应用中两种先验下获得一致的结论,两市收益和波动均存在星期工作日的异质性,从模型比较和预测效果来看适应性先验仍具优势.Starting from SV model normally used to describe volatility clustering,fat-tail T error of mean equation is set for financial data analysis application.Periodic heterogeneity phenomenon of financial time series is expressed by SV model with multiplying heterogenous volatility,in which periodic volatility plays the role of mixture parameter of SMN,and from which Bayesian posterior hierarchical is derived and used to estimate SV parameters.Two mixture parameter priors are tasted and compared with each other:The first is the IGamma(v/2,v/2)as the previous literature,the second is different from the previous studies,and called adaptable shrinkage prior based on the application background.In simulation,correct estimation results and the periodic heterogenous volatility are achieved by two priors,but the adaptable prior is clearly superior to the other one because it is more exact especially for fluctuation parameters analysis.By empirical analysis of Shanghai and Shenzhen stock markets,it is found that there exists day-of-week effect in returns and fluctuation series of both markets consistently under two priors.Adaptable prior shows still superior by model comparison and forecast effect.

关 键 词：SV模型 Bayesian分级模型 正态分布尺度混合(SMN) 混合参数 适应性先验 

分 类 号：O212[理学—概率论与数理统计]