跳跃的估计、股市波动率的预测以及预测精度评价

中国管理科学 ›› 2013, Vol. 21 ›› Issue (3): 50-60.

跳跃的估计、股市波动率的预测以及预测精度评价

杨科¹, 田凤平², 林洪³

1. 华南农业大学经济管理学院, 广东广州 510642;
2. 中山大学国际商学院, 广东广州 510275;
3. 广东商学院, 广东广州 510320

收稿日期:2011-12-30 修回日期:2012-10-11 出版日期:2013-06-30 发布日期:2013-06-20
基金资助:
国家自然科学基金资助项目(70971143,71203067);华南农业大学经济管理学院"211工程"青年项目(2012211QN03);中国博士后科学基金(2011M500134);广东省哲学社会科学规划项目(GD11YLJ01);中山大学青年教师起步资助计划(41000-3181404);2011年度中山大学人文社会科学青年教师桐山基金资助项目;广东省高等学校高层次人才项目;中山大学985工程三期建设项目金融创新与区域发展研究创新基地

Jump Estimation, Stock Market Volatility Forecasting and Prediction Accuracy Evaluation

YANG Ke¹, TIAN Feng-ping², LIN Hong³

1. College of Economics & Management, South China Agricultural University, Guangzhou 510642, China;
2. International Business School, Sun Yat-sen University, Guangzhou 510275, China;
3. Guangdong University of Business Studies, Guangzhou 510320, China

Received:2011-12-30 Revised:2012-10-11 Online:2013-06-30 Published:2013-06-20

摘要/Abstract

摘要： 本文基于C_TMPV理论估计已实现波动率的跳跃成分,在此基础上构建考虑跳跃的AHAR-RV-CJ模型和MIDAS-RV-CJ模型来预测中国股市的已实现波动率,并评价和比较各类波动率模型的预测精度。实证结果表明:基于C_TMPV估计的波动率跳跃成分对日、周以及月波动率的预测有显著的正向影响;AHAR-RV-CJ模型和MIDAS-RV-CJ模型的样本内和样本外预测精度在不同的预测时域上都是最高的,尤其是对数形式的模型;MIDAS族模型的样本外预测精度在中长期预测时域上比HAR族模型高;AHAR-RV-CJ模型和MIDAS-RV-CJ模型的样本外预测能力在中长期预测时域上比基于低频数据的Jump-GARCH模型、SV-CJ模型和SV-IJ模型好。

关键词: 波动率预测, 已实现波动率, C_TMPV, MIDAS 模型, SPA检验

Abstract: Based on the theory of corrected realized threshold multipower variation(C_TMPV), the jump components of the realized volatility are estimated, and two newly developed realized volatility model allowing for jump, the AHAR-RV-CJ model and MIDAS-RV-CJ model, are proposed to predict realized volatility of Chinese Stock Markets. The forecast accuracies of several volatility models are also evaluated and compared. Our findings demonstrate that the jump components of the realized volatility estimated by C_TMPV have positive and significant impacts on daily, weekly and monthly volatility prediction, and the AHAR-RV-CJ model and MIDAS-RV-CJ models with the continuous and jump components of the volatility are the best models for future volatility prediction in different prediction horizons. These results hold up for both the in-sample and out-of-sample forecasts, especially the logarithmic models. It is also found that the out-of-sample forecasting performance of MIDAS model is better than HAR model with the same regressor and the out-of-sample predictive power of AHAR-RV-CJ and MIDAS-RV-CJ models is better than Jump-GARCH, SV-CJ and SV-IJ models in the medium and long prediction horizons.

Key words: volatility forecasting, realized volatility, C_TMPV, MIDAS model, SPA test

中图分类号:

F830
F064.1

杨科, 田凤平, 林洪. 跳跃的估计、股市波动率的预测以及预测精度评价[J]. 中国管理科学, 2013, 21(3): 50-60.

YANG Ke, TIAN Feng-ping, LIN Hong. Jump Estimation, Stock Market Volatility Forecasting and Prediction Accuracy Evaluation[J]. Chinese Journal of Management Science, 2013, 21(3): 50-60.

参考文献

[1] Andersen T G, Bollerslev T, Diebod F X,et.al. Modelling and forecasting realized volatility [J]. Econometrica, 2003, 71(2): 579-625.
[2] Corsi F. A simple approximate long memory model of realized volatility[J]. Journal of Financial Econometrics, 2009, 7(2): 174-196.
[3] 徐正国,张世英. 调整"已实现"波动率与GARCH及SV模型对波动的预测能力的比较研究[J]. 系统工程,2004, 22(8): 60-63.
[4] 郭名媛,张世英. 赋权已实现波动及其长记忆、最优抽样频率选择 [J]. 系统工程学报, 2006, 21(6): 568-573.
[5] 魏宇,余怒涛. 中国股票市场的波动率预测模型及其SPA检验 [J]. 金融研究, 2007, 28(7): 138-150.
[6] 魏宇. 中国股票市场的最优波动率预测模型研究[J]. 管理学报, 2010, 7(6): 936-942.
[7] Andersen T G, Bollerslev T, Diebod F X. Roughing it up: Including jump components in the measurement, modeling, and forecasting of return volatility [J]. The Review of Economics and Statistics, 2007, 89(4): 701-720.
[8] Giot P, Laurent S. The information content of implied volatility in the light of the jump/continuous decomposition of realized volatility [J]. Journal of Future Markets, 2007, 27(3): 337-359.
[9] 王春峰,姚宁,房振明,等. 中国股市已实现波动率的跳跃行为研究 [J]. 系统工程, 2008, 26(2): 1-6.
[10] Shalen C T. Volume, volatility and dispersion of beliefs [J]. Review of Financial Studies, 1993, 6(2):405-434.
[11] Wang Jiang. A model of competitive stock trading volume [J]. Journal of Political Economy, 1994, 102(1):127-168.
[12] Buraschi A, Trojani F, Vedolin A. The joint behavior of credit spreads, stock options and equity returns when investors disagree [R]. Working Paper, Imperial College,2007.
[13] 杨科,陈浪南. 跳跃对中国股市波动率预测的影响研究[J]. 山西财经大学学报, 2010, 32(8): 39-48.
[14] Hansen P R, Lunde A. Realized variance and market microstructure noise[J]. Journal of Business and Economic Statistics, 2006, 24(2): 127-218.
[15] Barndor-Nielsen O E, Shephard N. Realized power variation and stochastic volatility [J]. Bernoulli, 2003, 9(2): 243-265.
[16] Barndor-Nielsen O E, Shephard N. Econometric analysis of realised covariation: high frequency covariance, regression and correlation in financial economics[J]. Econometrica, 2004, 72(3): 885-925.
[17] Barndor-Nielsen O E, Shephard N. Impact of jumps on returns and realized variances: econometric analysis of time-deformed levy process[J]. Journal of Econometrics, 2006, 131(1): 217-252.
[18] Huang Xin, Tauchen G. The relative contribution of jumps to total price variance[J]. Journal of Financial Econometrics, 2005, 3(4):456-499.
[19] Corsi F, Pirino D, Reno R. Threshold bipower variation and the impact of jumps on volatility forecasting[J]. Journal of Econometrics, 2010, 159(2):276-288.
[20] Forsberg L, Ghysels, E. Why do absolute returns predict volatility so well?[J]. Journal of Financial Econometrics, 2007, 5(1): 31-67.
[21] Ghysels E, Valkanov R. Linear time-series processes with mixed data sampling and MIDAS regression models [R]. Discussion paper, UNC and UCSD, 2006.
[22] Ghysels E, Santa-Clara P, Valkanov R. Predicting volatility: getting the most out of return data sampled at different frequencies[J]. Journal of Econometrics, 2006b, 131(1): 59-95.
[23] Ghysels E., Santa-Clara P, Valkanov R. MIDAS regressions: further results and new directions [J]. Econometric Reviews, 2007, 26(1): 53-90.
[24] Ghysels E, Santa-Clara P, Valkanov R. The MIDAS touch: mixed data sampling regression models[R]. Discussion paper, UNC and UCLA, 2010.
[25] Potton A J. Volatility forecast comparison using imperfect volatility proxies[J]. Journal of Econometrics, 2011, 160(1): 246-256.
[26] Hansen P R, Lunde A. A forecast comparison of volatility models: Does anything beat a GARCH(1,1)?[J]. Journal of Applied Econometrics, 2005, 20(7): 873-889.
[27] Maheu J M, Mc Curdy H. New arrival, jump dynamics and volatility components for individual stock returns[J]. Journal of Finance, 2004, 59(2): 755-793.
[28] Duffie D, Pan J, Singleton K. Transform analysis and asset pricing for affine jump-diffusions[J]. Econometrica, 2000, 68(6):1343-1376.
[29] Eraker B, Johannes M S, Polson N G. The impact of jumps in volatility and return[J]. Journal of Finance, 2003, 58(3):1269-1300.