我国股票市场波动性的实证研究
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摘要
波动性不仅普遍存在于金融时间序列之中,而且也是金融市场研究中的一个核心问题。用于进行波动性研究的模型主要有两类,一类是自回归条件异方差(ARCH)模型,另一类是随机波动(SV)模型。这两类模型都有各自的特点而且还存在众多的扩展模型,例如GARCH类模型和厚尾SV模型等。但是对于模拟我国金融时间序列,这两类模型及其众多的扩展模型的优劣并无一个定论。因此,需要引入了一系列的评价指标,对ARCH族模型和SV族模型的波动性预测能力进行比较分析。
本文分别讨论了两类波动计量模型的建模过程以及模型参数的估计方法。首先以深、沪股两市收益率数据为基础对ARCH族模型中的GARCH模型、TGARCH模型、EGARCH模型、均值GARCH模型等进行了实证分析。然后根据贝叶斯原理对SV族模型中的标准SV模型、SV-T模型、SV-GED模型进行了贝叶斯分析。构造基于Gibbs抽样的MCMC数值计算过程,通过WinBUGS软件对模型参数进行估计。对深、沪股市进行的比较分析发现,上海股市和深圳股市都表现出明显波动聚集性、非对称性和尖峰厚尾性。沪市的尖峰厚尾特点要强于深市,而深市的波动水平比沪市的要大,风险也更高。
最后利用RMSE、MAE、MAPE、TIC、LL、LE等评价指标对深证指数和上证指数在ARCH族和SV族模型下的模拟情况进行了样本外预测能力的比较。分析发现随机波动模型对我国股市的预测能力明显强于ARCH类模型。而且随机波动模型能够更好的描述收益率数据自身存在的尖峰厚尾性。另外,通过SV模型之间的比较发现,厚尾SV模型在深圳股市的预测效果要好于标准的SV模型。进一步比较发现,SV、SV-T、SV-GED三类SV模型中,大部分情况下预测能力最好的模型是SV-T模型。因此,我们可以得出结论,随机波动模型比ARCH模型更加适用于刻画我国股市的波动性特征。
The volatility is not only a universal phenomenon existing in the financial time series, but also a core research question to describing the financial market. There are two types of models used in researching financial volatility-autoregressive conditional heteroskedasitic (ARCH) model and stochastic volatility (SV) model. These two types of models have different characters and lots of expanding models, such as GARCH-type models、heavy-tail SV models and so on. But the quality of these models for simulating the financial time series does not have a conclusion. Therefore we need to introduce a series of indices to evaluate the accuracy of the forecasting ability of models.
This article introduced ARCH-type models, SV-type models and the method to estimate the parameters in these models. First, the GARCH model, the TGARCH model, the EGARCH model and the GARCH-M model in the ARCH model system were analyzed, which is based on the data of returns ratio series of Shanghai stock market and Shenzhen stock market. Then, the SV-N model, the SV-T model, the SV-GED model in the SV model system were analyzed according to the Bayesian theorem. A Markov chain Monte Carlo algorithm procedure with Gibbs sampler was designed to estimate the models' parameter through the WinBUGS software. After the comparative analysis between Shanghai and Shenzhen stock market, we discovery that Shanghai Stock market and Shenzhen Stock market all display the strong cluster effect, leverage effect and leptokurtic effect. Shanghai Stock market has the stronger leptokurtic effect compared to Shenzhen Stock market. But the Shenzhen Stock market's volatility level is higher than Shanghai Stock market, the risk is also higher.
The out-of-sample forecasting ability of ARCH models system were compared with SV models system using the RMSE, MAE, MAPE, TIC, LL, LE indices under the Shanghai and Shenzhen Stock market. The analysis discovered that the forecasting ability of SV models is superior than ARCH models. And SV models can profoundly descript the leptokurtic effect in our country Stock market better. In the SV models, the forecasting accuracy of Heavy-ail SV model is superior than the SV-N model in Shenzhen Stock market. At most times, the best model to forecast the volatility of Stock market is the SV-T model. Therefore, we may draw the conclusion, stochastic volatility model is more fit for descript our country Stock market's volatility characteristics.
本文分别讨论了两类波动计量模型的建模过程以及模型参数的估计方法。首先以深、沪股两市收益率数据为基础对ARCH族模型中的GARCH模型、TGARCH模型、EGARCH模型、均值GARCH模型等进行了实证分析。然后根据贝叶斯原理对SV族模型中的标准SV模型、SV-T模型、SV-GED模型进行了贝叶斯分析。构造基于Gibbs抽样的MCMC数值计算过程,通过WinBUGS软件对模型参数进行估计。对深、沪股市进行的比较分析发现,上海股市和深圳股市都表现出明显波动聚集性、非对称性和尖峰厚尾性。沪市的尖峰厚尾特点要强于深市,而深市的波动水平比沪市的要大,风险也更高。
最后利用RMSE、MAE、MAPE、TIC、LL、LE等评价指标对深证指数和上证指数在ARCH族和SV族模型下的模拟情况进行了样本外预测能力的比较。分析发现随机波动模型对我国股市的预测能力明显强于ARCH类模型。而且随机波动模型能够更好的描述收益率数据自身存在的尖峰厚尾性。另外,通过SV模型之间的比较发现,厚尾SV模型在深圳股市的预测效果要好于标准的SV模型。进一步比较发现,SV、SV-T、SV-GED三类SV模型中,大部分情况下预测能力最好的模型是SV-T模型。因此,我们可以得出结论,随机波动模型比ARCH模型更加适用于刻画我国股市的波动性特征。
The volatility is not only a universal phenomenon existing in the financial time series, but also a core research question to describing the financial market. There are two types of models used in researching financial volatility-autoregressive conditional heteroskedasitic (ARCH) model and stochastic volatility (SV) model. These two types of models have different characters and lots of expanding models, such as GARCH-type models、heavy-tail SV models and so on. But the quality of these models for simulating the financial time series does not have a conclusion. Therefore we need to introduce a series of indices to evaluate the accuracy of the forecasting ability of models.
This article introduced ARCH-type models, SV-type models and the method to estimate the parameters in these models. First, the GARCH model, the TGARCH model, the EGARCH model and the GARCH-M model in the ARCH model system were analyzed, which is based on the data of returns ratio series of Shanghai stock market and Shenzhen stock market. Then, the SV-N model, the SV-T model, the SV-GED model in the SV model system were analyzed according to the Bayesian theorem. A Markov chain Monte Carlo algorithm procedure with Gibbs sampler was designed to estimate the models' parameter through the WinBUGS software. After the comparative analysis between Shanghai and Shenzhen stock market, we discovery that Shanghai Stock market and Shenzhen Stock market all display the strong cluster effect, leverage effect and leptokurtic effect. Shanghai Stock market has the stronger leptokurtic effect compared to Shenzhen Stock market. But the Shenzhen Stock market's volatility level is higher than Shanghai Stock market, the risk is also higher.
The out-of-sample forecasting ability of ARCH models system were compared with SV models system using the RMSE, MAE, MAPE, TIC, LL, LE indices under the Shanghai and Shenzhen Stock market. The analysis discovered that the forecasting ability of SV models is superior than ARCH models. And SV models can profoundly descript the leptokurtic effect in our country Stock market better. In the SV models, the forecasting accuracy of Heavy-ail SV model is superior than the SV-N model in Shenzhen Stock market. At most times, the best model to forecast the volatility of Stock market is the SV-T model. Therefore, we may draw the conclusion, stochastic volatility model is more fit for descript our country Stock market's volatility characteristics.
引文
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[2] Fama E F, Mandelbrot. The Stable Paretain Distribution. Journal of Business, 1965(36): 420-429
[3] J Engle R F. Autoregressive conditional heteroskedas—ticity with estimates of the variance of U. K. inflation. Econometrica, 1982, 50(4): 987-1008
[4] Bollerslev. Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 1986(31):307-327
[5] Berndt E K, hall R E. Nonlinear Strucural Models.Annald of Economic and social measurement, 1974(81):637-54
[6] Press W H, Teukolsy. Vetterling Numerical Recipes in Fortran. Cambridge University press, 1992(12),231-265
[7] Engle R F, Lilien D M and Robins R P. Estimating Time Varying Risk Rreamia in the term Structure the ARCH-Mmodel. Econometrica, 1987(55):391-407
[8] Pagan A R., Schwet G W Alternative Models for conditional Stock volatilities. Junrnal of Econometrics, 1990(45):267-90
[9] Nelson D B. conditional Heteroskeda sticity in Asset Returns-A new approach. Econometrica, 1991(59):347-70
[10] Glosten L R, Jagannathan R and Runkle P E. on the Relation Between the expected Value and the volatility of the Nominal excess Return on stocks. The Journal of Finance, 1993(45): 1779-1801
[11] Engle R F and Ng V K. Measuring and testing the Impact of New on volatility. Journal of Finance, 1993(48): 1749-78
[12] Day T E and Lewis C M. stock market volatility and the information content of stock index options. Journal of Econometrics, 1992(52):267-87
[13] Clark K Y and Thomas S H. the integration and Efficiency of international Bond markets. Journal of Business, 1973(36):431-50
[14] Tauchen H and Pitts M F. Threshold Models in nonlinear Time series Analysis. Springer, 1983(35):271-360
[15] Danielsson A C and Hinkley D V. Bootstrap Methods and their Application. Cambridge University Press,cambridge
[16] Harvey A ,Ruiz E and shephard N. Multivariate stochastic Variance Models. review of Economic Studies, 1994(61):274-64
[17] Chou K Y, short-Run Forecasting of commodity price: An application of Autoregressive moving average models. IMF staff papers, 1988(25):90-111
[18] Pegennaro C N, Baillie M E. further evidence on investor overreaction and stock market Seasonality. Journal of Finance, 1990(40): 763-805
[19] Pangan A R and Kearns P S. The Econometrics of Financial Market.Journal of empirical Finance, 1993 (3): 15-102
[20] Akgiray V. conditional Heteroskedasticity in Time series of stock Retuns. Evidence and Forecasts Journal of Business, 1989(62): 55-80
[21]West K D and cho D.The predictive Ability of several Models of Exchage rate Volatility.Journal of Econometrics,1995(69):367-91
[22]Franses P H and Vandijk D.Forecasting Stock Market Volatility Using Non-Linear GARCH models.Journal of Forecasting,1996(15):229-35
[23]Brailsford F J,Faff.J C.Comparing information in forecasting from Economics.Journal of Econometrics.1996(32):243-8
[24]Gibson M S and Boyer B H.Evaluating Forecasts of correlation Using option pricing.Journal of Derivatives,Winter,18-38.
[25]Brooks C.Forecasting stock Return volatility:Does volume Help.Journal of Forecasting,1998(17):59-80
[26]陈千里,周少甫.中国股市收益率与波动性长记忆性的实证研究.金融理论与实践,2003,2-9
[27]胡海鹏,方兆本.AR-EGARCH-M模型对中国股市波动性的拟和分析.系统工程,2002,22(3):47-51
[28]刘宁.对上海股票市场波动性的ARCH研究.兰州大学学报,2004,15(6):44-48
[29]莫阳.股票市场波动性得国际比较研究.数量经济技术经济研究,2004,24(10):43-46
[30]朱孔来,倪杰.中国沪深股市收益率波动性的实证分析.经济学,2002,36-39
[31]张维,张小涛.不对称的GARCH模型对中国股市波动性的研究.经济研究,2004,8(4):76-81
[32]王春峰,蒋祥林,吴晓霖.基于状态转移ARCH模型的中国股市波动性研究.系统工程学报,2005,15(1),24-27
[33]胡海鹏,方兆本.GARCH-NLS模型对我国股市的实证分析.管理科学学报,2001,67-70
[34]田益祥,庄作钦.中国股票市场短期ARCH效应研究、金融研究,2001年,9(5):58-62
[35]鲁万波,李竹渝.基于非参数核回归估计方法对中国股市波动性的实证研究.世界经济,2000,13(11):44-47
[36]王春峰,蒋祥林,李刚.基于随机波动性模型的中国股市波动性估计.管理科学学报,2003,216-219
[37]丁忠明,夏万军.CARR模型和GARCH模型波动性预测能力比较.数量经济技术经济研究,2005,53-55
[38]郑梅,苗佳,王升华.GARCH族模型的波动性预测能力比较.统计研究,2005,79-83
[39]Black F And scholes M.the pricing of option and corporate liabilities.Journal of political Economy,1976(81):637-54
[40]Zakoian P.Seasonlity and stock market overreaction.Journal of Financial and Quantitative Analysis.1990(25):113-25
[41]Dimson E and March P.volatility Forecasting without Datasnooping.Journal of Banking and Finance,1990(14):399-421
[2] Fama E F, Mandelbrot. The Stable Paretain Distribution. Journal of Business, 1965(36): 420-429
[3] J Engle R F. Autoregressive conditional heteroskedas—ticity with estimates of the variance of U. K. inflation. Econometrica, 1982, 50(4): 987-1008
[4] Bollerslev. Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 1986(31):307-327
[5] Berndt E K, hall R E. Nonlinear Strucural Models.Annald of Economic and social measurement, 1974(81):637-54
[6] Press W H, Teukolsy. Vetterling Numerical Recipes in Fortran. Cambridge University press, 1992(12),231-265
[7] Engle R F, Lilien D M and Robins R P. Estimating Time Varying Risk Rreamia in the term Structure the ARCH-Mmodel. Econometrica, 1987(55):391-407
[8] Pagan A R., Schwet G W Alternative Models for conditional Stock volatilities. Junrnal of Econometrics, 1990(45):267-90
[9] Nelson D B. conditional Heteroskeda sticity in Asset Returns-A new approach. Econometrica, 1991(59):347-70
[10] Glosten L R, Jagannathan R and Runkle P E. on the Relation Between the expected Value and the volatility of the Nominal excess Return on stocks. The Journal of Finance, 1993(45): 1779-1801
[11] Engle R F and Ng V K. Measuring and testing the Impact of New on volatility. Journal of Finance, 1993(48): 1749-78
[12] Day T E and Lewis C M. stock market volatility and the information content of stock index options. Journal of Econometrics, 1992(52):267-87
[13] Clark K Y and Thomas S H. the integration and Efficiency of international Bond markets. Journal of Business, 1973(36):431-50
[14] Tauchen H and Pitts M F. Threshold Models in nonlinear Time series Analysis. Springer, 1983(35):271-360
[15] Danielsson A C and Hinkley D V. Bootstrap Methods and their Application. Cambridge University Press,cambridge
[16] Harvey A ,Ruiz E and shephard N. Multivariate stochastic Variance Models. review of Economic Studies, 1994(61):274-64
[17] Chou K Y, short-Run Forecasting of commodity price: An application of Autoregressive moving average models. IMF staff papers, 1988(25):90-111
[18] Pegennaro C N, Baillie M E. further evidence on investor overreaction and stock market Seasonality. Journal of Finance, 1990(40): 763-805
[19] Pangan A R and Kearns P S. The Econometrics of Financial Market.Journal of empirical Finance, 1993 (3): 15-102
[20] Akgiray V. conditional Heteroskedasticity in Time series of stock Retuns. Evidence and Forecasts Journal of Business, 1989(62): 55-80
[21]West K D and cho D.The predictive Ability of several Models of Exchage rate Volatility.Journal of Econometrics,1995(69):367-91
[22]Franses P H and Vandijk D.Forecasting Stock Market Volatility Using Non-Linear GARCH models.Journal of Forecasting,1996(15):229-35
[23]Brailsford F J,Faff.J C.Comparing information in forecasting from Economics.Journal of Econometrics.1996(32):243-8
[24]Gibson M S and Boyer B H.Evaluating Forecasts of correlation Using option pricing.Journal of Derivatives,Winter,18-38.
[25]Brooks C.Forecasting stock Return volatility:Does volume Help.Journal of Forecasting,1998(17):59-80
[26]陈千里,周少甫.中国股市收益率与波动性长记忆性的实证研究.金融理论与实践,2003,2-9
[27]胡海鹏,方兆本.AR-EGARCH-M模型对中国股市波动性的拟和分析.系统工程,2002,22(3):47-51
[28]刘宁.对上海股票市场波动性的ARCH研究.兰州大学学报,2004,15(6):44-48
[29]莫阳.股票市场波动性得国际比较研究.数量经济技术经济研究,2004,24(10):43-46
[30]朱孔来,倪杰.中国沪深股市收益率波动性的实证分析.经济学,2002,36-39
[31]张维,张小涛.不对称的GARCH模型对中国股市波动性的研究.经济研究,2004,8(4):76-81
[32]王春峰,蒋祥林,吴晓霖.基于状态转移ARCH模型的中国股市波动性研究.系统工程学报,2005,15(1),24-27
[33]胡海鹏,方兆本.GARCH-NLS模型对我国股市的实证分析.管理科学学报,2001,67-70
[34]田益祥,庄作钦.中国股票市场短期ARCH效应研究、金融研究,2001年,9(5):58-62
[35]鲁万波,李竹渝.基于非参数核回归估计方法对中国股市波动性的实证研究.世界经济,2000,13(11):44-47
[36]王春峰,蒋祥林,李刚.基于随机波动性模型的中国股市波动性估计.管理科学学报,2003,216-219
[37]丁忠明,夏万军.CARR模型和GARCH模型波动性预测能力比较.数量经济技术经济研究,2005,53-55
[38]郑梅,苗佳,王升华.GARCH族模型的波动性预测能力比较.统计研究,2005,79-83
[39]Black F And scholes M.the pricing of option and corporate liabilities.Journal of political Economy,1976(81):637-54
[40]Zakoian P.Seasonlity and stock market overreaction.Journal of Financial and Quantitative Analysis.1990(25):113-25
[41]Dimson E and March P.volatility Forecasting without Datasnooping.Journal of Banking and Finance,1990(14):399-421