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

Abstract

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

CLC Number:

F830

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.

References

[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.

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

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