动态金融高阶矩建模:基于Generalized-t分布和Gram-Charlier展开分布的比较研究

doi:10.16381/j.cnki.issn1003-207x.2015.10.002

中国管理科学 ›› 2015, Vol. 23 ›› Issue (10): 11-18.doi: 10.16381/j.cnki.issn1003-207x.2015.10.002

动态金融高阶矩建模:基于Generalized-t分布和Gram-Charlier展开分布的比较研究

黄卓, 李超

北京大学国家发展研究院中国经济研究中心, 北京 100871

收稿日期:2014-07-12 修回日期:2015-04-17 出版日期:2015-10-20 发布日期:2015-10-24
作者简介:黄卓(1978-),男(汉族),湖北武汉人,北京大学国家发展研究院中国经济研究中心助理教授、博士生导师,经济学博士,研究方向:金融计量经济学.
基金资助:
国家自然科学基金青年科学基金资助项目(71201001);教育部人文社会科学青年基金资助项目(12YJC790073)

Modeling Dynamic Financial Higher Moments: A Comparison Study Based on Generalized-t Distribution and Gram-Charlier Expansion

HUANG Zhuo, LI Chao

National School of Development, Peking University, Beijing 100871, China

Received:2014-07-12 Revised:2015-04-17 Online:2015-10-20 Published:2015-10-24

摘要/Abstract

摘要： 动态时变高阶矩是金融收益率的一个重要特征。本文对比研究了主流的Generalized-t分布(GT)和Gram Charlier Expansion分布(GCE)在GJRGARCH模型下对动态高阶矩的拟合能力和Value-at-Risk的预测能力。基于2005-2014美国标普500股指和中国沪深300股指日收益率的实证结果显示,收益率的条件高阶矩存在显著的时变性和持续性,其中偏度参数的持续性参数达到0.9以上。从各种统计指标综合来看,这两种方法都具有较好的实证表现。尽管GCE分布具有某些高阶矩建模的便利性,GT分布的实证拟合能力更强,对极端概率Value-at-Risk的样本外预测也更加准确。

关键词: 高阶矩, GJRGARCH, Generalized-t分布, Gram Charlier Expansion

Abstract: Dynamic higher moments is a stylized feature of financial returns. Empirical performance of the popular Generalized-t distribution (GT) and the Gram-Charlier series expansion of the Gaussian density (GCE) under GJRGARCH framework are compared in this paper, in terms of their capacity to fit time-varying higher moments and forecast Value-at-Risk. Using the daily returns of S&P 500 stock index in the U.S. and CSI300 stock index in China, it's shown that both return series exhibit time variation and persistence in conditional higher moments, and the persistence parameters of skewness are as high as 0.9. According to various statistical standards, both GT and GCE distribution have good empirical performance. GT models slightly outperform GCE models in fitting return distribution and forecasting extreme Value-at-Risk out-of-sample, despite some modeling advantages of GCE.

Key words: higher moments, GJRGARCH, generalized-t distribution, gram charlier expansion

中图分类号:

F830

黄卓, 李超. 动态金融高阶矩建模:基于Generalized-t分布和Gram-Charlier展开分布的比较研究[J]. 中国管理科学, 2015, 23(10): 11-18.

HUANG Zhuo, LI Chao. Modeling Dynamic Financial Higher Moments: A Comparison Study Based on Generalized-t Distribution and Gram-Charlier Expansion[J]. Chinese Journal of Management Science, 2015, 23(10): 11-18.

参考文献

[1] Hansen B E. Autoregressive conditional density estimation[J]. International Economic Review, 1994,35(3):705-730.

[2] Harvey C R, Siddique A. Autoregressive conditional skewness[J]. Journal of Financial and Quantitative Analysis,1999, 34(4):465-487.

[3] Jondeau E, Rockinger M. Conditional volatility, skewness, and kurtosis:Existence, persistence, and comovements[J]. Journal of Economic Dynamics and Control, 2003,27(10):1699-1737.

[4] Brooks C, Burke S P, Heravi S, et al. Autoregressive conditional kurtosis[J]. Journal of Financial Econometrics, 2005,3(3):399-421.

[5] Bali T G, Mo Hengyang, Tang Yi. The role of autoregressive conditional skewness and kurtosis in the estimation of conditional VaR[J]. Journal of Banking and Finance, 2008,32(2):269-282.

[6] Dark J G. Estimation of time varying skewness and kurtosis with an application to value at risk[J]. Studies in Nonlinear Dynamics and Econometrics, 2010,14(2):3-48.

[7] Jondeau E, Rockinger M. The impact of shocks on higher moments[J]. Journal of Financial Econometrics, 2009,7(2):77-105.

[8] Jondeau E, Rockinger M. On the importance of time variability in higher moments for asset allocation[J]. Journal of Financial Econometrics, 2012,10(1):84-123.

[9] 庄泓刚. 基于非正态分布的动态金融波动性模型研究[D]. 天津:天津大学, 2008.

[10] Leon A, Rubio G, Serna G. Autoregresive conditional volatility, skewness and kurtosis[J]. The Quarterly Review of Economics and Finance, 2005,45(4):599-618.

[11] 许启发. 高阶矩波动性建模及应用[J]. 数量经济技术经济研究, 2006,23(12):135-145.

[12] 许启发, 张世英. 多元条件高阶矩波动性建模[J]. 系统工程学报, 2007,22(1):1-8.

[13] 王鹏, 王建琼, 魏宇. 自回归条件方差-偏度-峰度:一个新的模型[J]. 管理科学学报, 2009,12(5):121-129.

[14] 王鹏, 魏宇, 王建琼. 不同矩属性波动模型对中国股市波动率的预测精度分析[J]. 数理统计与管理, 2010,(3):550-559.

[15] 王鹏. 基于时变高阶矩波动模型的VaR与ES度量[J]. 管理科学学报, 2013,16(2):33-45.

[16] Gabrielsen A, Zagaglia P, Kirchner A, et al. Forecasting Value-at-Risk with time-varying variance, skewness and kurtosis in an exponential weighted moving average framework[R]. Working Paper, Dipartimento Scienze Economiche,Universita'di:Bologna,2012.

[17] Polanski A, Stoja E. Incorporating higher moments into Value-at-Risk forecasting[J]. Journal of Forecasting, 2010,29(6):523-535.

[18] Niguez T, Perote J. Forecasting heavy-tailed densities with positive edgeworth and gram Charlier expansions[J]. Oxford Bulletin of Economics and Statistics, 2012,74(4):600-627.

[19] Lanne M, Pentti S. Modeling conditional skewness in stock returns[J]. The European Journal of Finance, 2007,13(8):691-704.

[20] Ergun A T, Jun J. Time-varying higher-order conditional moments and forecasting intraday VaR and Expected Shortfall[J]. The Quarterly Review of Economics and Finance, 2010b,50(3):264-272.

[21] Gerlach R, Lu Zudi, Huang Hai. Exponentially smoothing the Skewed Laplace distribution for Value-at-Risk forecasting[J]. Journal of Forecasting, 2013,32(6):534-550.

[22] Yan Jun. Asymmetry, fat-tail, and autoregressive conditional density in financial return data with systems of frequency curves[R]. Working Paper, University of Lowa,2005.

[23] 蒋翠侠. 基于JSU分布的广义自回归条件密度建模及应用[J]. 数量经济技术经济研究, 2008,25(8):137-150.

[24] 蒋翠侠, 张世英. 金融高阶矩风险溢出效应研究[J]. 中国管理科学,2009, 17(1):17-28.

[25] Feunou B, Jahan-Parvar M R, Tedongap R. Which parametric model for conditional skewness?[J]. The European Journal of Finance,2014, (ahead-of-print):1-35.

[26] Wilhelmsson A. Density forecasting with time varying higher moments:A model confidence set approach[J]. Journal of Forecasting, 2013,32(1):19-31.

[27] Engle R F. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation[J]. Econometrica:Journal of the Econometric Society,1982, 50(4):987-1007.

[28] Bollerslev T. Generalized autoregressive conditional heteroskedasticity[J]. Journal of Econometrics, 1986,31(3):307-327.

[29] Hong Yongmiao, Li Haitao. Nonparametric specification testing for continuous-time models with applications to term structure of interest rates[J]. Review of Financial Studies, 2005,18(1):37-84.

[30] Ergun A T, Jun J. Conditional skewness, kurtosis, and density specification testing:Moment-based versus Nonparametric tests[J]. Studies in Nonlinear Dynamics and Econometrics, 2010a,14(3):1-19.

[31] Ergun A T. Skewness and kurtosis persistence:Conventional vs. robust measures[R]. Working paper, Midwest Finance Association,2011.

动态金融高阶矩建模:基于Generalized-t分布和Gram-Charlier展开分布的比较研究

Modeling Dynamic Financial Higher Moments: A Comparison Study Based on Generalized-t Distribution and Gram-Charlier Expansion

PDF (PC)

可视化

被引次数

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 8

Metrics

本文评价

推荐阅读 0

[1]	黄光麟,鲁万波. 基于变系数多因子半参数分布的高维动态高阶矩投资组合研究[J]. 中国管理科学, 2023, 31(12): 272-280.
[2]	吴金宴, 王鹏. 基于协高阶矩检验体系的中国资本市场开放与风险传染效应研究[J]. 中国管理科学, 2023, 31(1): 37-46.
[3]	林娟娟, 唐勇, 周小亮, 朱鹏飞. 北上资金、百度指数与股市关联性的时频域研究——基于协高阶矩视角[J]. 中国管理科学, 2022, 30(1): 20-31.
[4]	鲁万波, 黄光麟, Kris Boudt. 股市涨跌预测与量化投资策略:基于时变矩成分分析[J]. 中国管理科学, 2020, 28(2): 1-12.
[5]	朱鹏飞, 唐勇, 钟莉. 基于小波-高阶矩模型的投资组合策略——以国际原油市场为例[J]. 中国管理科学, 2020, 28(10): 24-35.
[6]	方立兵, 曾勇. 股市收益率高阶矩风险的产生机制检验[J]. 中国管理科学, 2016, 24(4): 27-36.
[7]	蒋翠侠, 张世英. 金融高阶矩风险溢出效应研究[J]. 中国管理科学, 2009, 17(1): 17-28.
[8]	蒋翠侠, 许启发, 张世英. 金融市场条件高阶矩风险与动态组合投资[J]. 中国管理科学, 2007, 15(1): 27-33.