中国股票市场主要转折点的识别:基于改进的小波领袖法与逼近技术的贝叶斯法

doi:10.16381/j.cnki.issn1003-207x.2018.12.002

中国管理科学 ›› 2018, Vol. 26 ›› Issue (12): 12-24.doi: 10.16381/j.cnki.issn1003-207x.2018.12.002

中国股票市场主要转折点的识别:基于改进的小波领袖法与逼近技术的贝叶斯法

谭政勋¹, 黄锦东², 叶诚²

1. 湖南师范大学商学院, 湖南长沙 410002;
2. 暨南大学经济学院, 广东广州 510062

收稿日期:2017-07-29 修回日期:2017-12-13 出版日期:2018-12-20 发布日期:2019-02-25
通讯作者: 谭政勋(1970-),男(汉族),湖南邵阳人,湖南师范大学"潇湘学者"特聘教授,商学院金融系主任,博士生导师,研究方向:资产价格的长期记忆与预测,E-mail:tzxun1810@163.com. E-mail:tzxun1810@163.com
基金资助:
国家自然科学基金资助项目（71773035）；中央高校基本科研业务费专项资金资助（15JNYH009）；广东省自然科学基金资助项目（2015A030313338）

Identifying the Main Turning Point of Stock Market: Based on improved Wavelet Leader and Bayesian Estimation of Approximation Technique

TAN Zheng-xun¹, HUANG Jing-dong², YE Cheng²

1. Hunan NormalUniversity, College of Business, Changsha 410002, China;
2. Jinan University, College of Economics, Guangzhou 510062, China

Received:2017-07-29 Revised:2017-12-13 Online:2018-12-20 Published:2019-02-25

摘要/Abstract

摘要： 在探讨单重分形模型与以小波领袖法为代表的多重分形模型的内在联系的基础上，分析了小波领袖法的内在缺陷并提出了改进方法，并利用Monte Carlo模拟比较了传统的小波领袖法和改进的小波领袖法的效果；在改进的小波领袖法的框架下，利用基于逼近技术的贝叶斯法估计了上证指数收益率序列的多重分形谱及有关参数。理论分析表明，在传统小波领袖法中，小波母函数"能量和为1"，这与经典的R/S法以及实际股票市场的实际情况都不相符，且会严重低估标度指数。实证表明，改进的小波领袖法克服了对标度指数的低估效应和对多重分形谱估计值的扭曲；在利用改进的小波领袖法刻画股票市场的波动性后，基于逼近技术的贝叶斯估计法不仅减少了需要估计的参数，而且准确识别了我国股票市场长期趋势发生变化的主要转折点，结果也非常稳健。

关键词: 股票市场, 主要转折点, 小波领袖法, 逼近技术, 贝叶斯估计法

Abstract: By discussing the connections between mono-fractal model and multi-fractal model as represented by wavelet leader, intrinsic weaknesses of wavelet leader method are analyzed to make an improvement, and Monte Carlo simulation is used to compare the effect between traditional wavelet leader method and improved wavelet leader method. Within the framework of improved wavelet leader method. Bayesian estimation based on Approximation technique is used to compute the multifractal spectrum and the related parameters of the return rate series of the Shanghai Composite Index.Our theoretical analysis indicates that in the conventional wavelet leader method, the setting-wavelet sum of energy equals one-leads to inconsistence with both canonical R/S analysis method and the actual situation of the real stock market. Thus, conventional wavelet leader method can cause a significant underestimation of scaling index and other adverse outcomes. Under the improved wavelet leader method, based on approximation technology, Bayesian estimation method can not only reduce the parameters that need to be estimated, but also identify the significant turning point of China's stock market, and the result is also very robust.

Key words: stock market, significant turning point, wavelet leader method, approximation technique, Bayesian estimation

中图分类号:

F830

谭政勋, 黄锦东, 叶诚. 中国股票市场主要转折点的识别:基于改进的小波领袖法与逼近技术的贝叶斯法[J]. 中国管理科学, 2018, 26(12): 12-24.

TAN Zheng-xun, HUANG Jing-dong, YE Cheng. Identifying the Main Turning Point of Stock Market: Based on improved Wavelet Leader and Bayesian Estimation of Approximation Technique[J]. Chinese Journal of Management Science, 2018, 26(12): 12-24.

参考文献

[1] Fama E F. Efficient capital markets:A review of theory and empirical work[J]. The Journal of Finance, 1970, 25(2):383-417.

[2] Shiller R J. Do stock prices move too much to be justified by subsequent changes in dividends?[J]. The American Economic Review, 1981,71(3):421-436.

[3] Peters E E. Peters D. Fractal market analysis:Applying chaos theory to investment and economics[M]. Hobken, New Jersey, USA:John Wiley & Sons, 1994.

[4] Peters E E. Chaos and order in the capital markets:A new view of cycles, prices, and market volatility[M]. Hobken, New Jersey, USA:John Wiley & Sons, 1996.

[5] Mandelbrot B. Forecasts of future prices, unbiased markets, and "martingale" models[J]. The Journal of Business, 1966, 39(1):242-255.

[6] Mandelbrot B. A statistical methodology for non-periodic cycles:From the covariance to R/S analysis[M].Cambridge, MA, USA:National Bureau ofEconomic Research, Inc, 2009:259-290.

[7] Lo A W. Long-Term Memory in Stock Market Prices[J]. Econometrica, 1991, 59(5):1279-1313.

[8] Giraitis L, Kokoszka P, Leipus R, et al. Rescaled variance and related tests for long memory in volatility and levels[J].Journal of Econometrics, 2003, 112(2):265-294.

[9] Grech D, Mazur Z. Can one make any crash prediction in finance using the local Hurst exponent idea?[J]. Physica A:Statistical Mechanics and Its Applications, 2012, 336(1):133-145.

[10] Grech D, Pamu?a G. The local Hurst exponent of the financial time series in the vicinity of crashes on the Polish stock exchange market[J]. Physica A:Statistical Mechanics and Its Applications, 2008, 387(16-17):4299-4308.

[11] Kristoufek L. Local scaling properties and market turning points at prague stock exchange[J]. Acta PhysicaPolonica, 2010, 42(6):1223-1236.

[12] Bacry E, Delour J, Muzy J F. Modelling financial time series using multifractal random walks[J]. Physica A:Statistical Mechanics and Its Applications, 2001, 299(1):84-92.

[13] Kantelhardt J W, Zsehiegner S A, Koseielny B E, et al. Multifractal detrended fluctuation analysis of nonstationary time series[J]. Physica A:Statistical Mechanics and Its Applications, 2002,5(316):87-114.

[14] 苑莹,庄新田,金秀.基于MF-DFA的中国股票市场多标度特性及成因分析[J].管理工程学报,2009,23(4):96-99.

[15] Muzy J F, Bacry E, Arneodo A. Multifractal formalism for fractal signals:The structure-function approach versus the wavelet-transform modulus-maxima method[J]. Physical Review E, 1993, 47(2):875-884.

[16] Jaffard S, Lashermes B, Abry P. Wavelet leaders in multifractal analysis[M]//Qian Tao, Vai M I, Xu Yuesheng(eds). Wavelet analysis and applications. Switzerland:Birkhäuser Basel, 2006:201-246.

[17] Ramsey J B, Usikov D, Zaslavsky G M. An analysis of U.S. stock price behavior using wavelets[J]. Fractals,1995, 3(2):377-389.

[18] Pavlov A N, Ebeling W, Molgedey L, et al. Scaling features of texts, images and time series[J]. Physica A:Statistical Mechanics and Its Applications, 2001, 300(1):310-324.

[19] 王哲, 王春峰, 顾培亮. 小波分析在股市数据分析中的应用[J]. 系统工程学报, 1999, 14(3):286-289.

[20] 周明磊.非参数估计与小波分析在股市趋势线中的应用[J]. 数理统计与管理, 2005,25(4):70-75.

[21] 梁强, 范英, 魏一鸣.基于小波分析的石油价格长期趋势预测方法及其实证研究[J].中国管理科学,2005,13(1):30-36.

[22] 樊颖,张红,杨赞.基于小波分析的北京市住宅市场景气循环周期[J]. 清华大学学报:自然科学版, 2015,(9):984-990.

[23] 刘向丽,王旭朋.基于小波分析的股指期货高频预测研究[J].系统工程理论与实践,2015,35(6):1425-1432.

[24] Mallat S. A wavelet tour of signal processing:the sparse way[M]. Academic press, 2008.

[25] Wood A T A, Chan G. Simulation of stationary Gaussian processes in[0, 1]^d[J]. Journal of Computational and Graphical Statistics, 1994, 3(4):409-432.

[26] Wendt H, Dobigeon N, Tourneret J Y, et al. Bayesian estimation for the multifractality parameter[C]//Proceedings of 2013 IEEE International Conference on Acoustics, Speech and Signal Processing. Vancouver, BC, Canada, May 26-31, 2013:6556-6560.

[27] Wendt H, Jaffard S, Abry P. Multifractal analysis of self-similar processes[C]//Proceedings of 2012 Statistical Signal Processing Workshop.Ann Arbor, MI, USA, Aug 5-8, 2012:69-72.

[28] Combrexelle S, Wendt H, Dobigeon N, et al. Bayesian estimation of the multifractality parameter for image texture using a whittle approximation[J]. IEEE Transctions on Image Processing, 2015, 24(8):2540-2551.

[29] Liu J S. Monte Carlo strategies in scientific computing[M]. Berlin Springer Science & Business Media, 2008.

[30] Brooks S, Gelman A, Jones G L, et al. Handbook of Markov chain Monte Carlo[J]. Chance, 2011, 25(1):53-55.

[31] 夏南新. 基于分形R/S技术的中国股市非规则周期性研究[J]. 统计研究, 2006,(2):28-31.

[32] 谭政勋, 张欠. 中国股票市场的长期记忆性与趋势预测研究[J]. 统计研究, 2016, 33(10):57-66.

[33] Zheng Xiaolian, Chen B M. Stock market modeling and forecasting[M]. London:Springer, 2013.

中国股票市场主要转折点的识别:基于改进的小波领袖法与逼近技术的贝叶斯法

Identifying the Main Turning Point of Stock Market: Based on improved Wavelet Leader and Bayesian Estimation of Approximation Technique

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 10

[1]	唐振鹏, 吴俊传, 冉梦, 张婷婷. 考虑投资者情绪的中国股市自激发效应研究[J]. 中国管理科学, 2020, 28(7): 1-12.
[2]	谢赤, 胡雪晶, 王纲金. 金融危机10年来中国股市动态演化与市场稳健研究——一个基于复杂网络视角的实证[J]. 中国管理科学, 2020, 28(6): 1-12.
[3]	陈其安, 张慧, 陈抒妤. 股指期货交易加剧了中国股票市场波动性吗？——基于投资者结构的理论和实证研究[J]. 中国管理科学, 2020, 28(4): 1-13.
[4]	刘凤根, 吴军传, 杨希特, 欧阳资生. 基于混频数据模型的宏观经济对股票市场波动的长期动态影响研究[J]. 中国管理科学, 2020, 28(10): 65-76.
[5]	尹海员, 朱旭. 投资者异质信念、预期演化与股票市场流动性[J]. 中国管理科学, 2019, 27(10): 12-21.
[6]	罗嘉雯, 陈浪南. 多国股票市场的高频波动相关性研究[J]. 中国管理科学, 2018, 26(2): 116-125.
[7]	黄书培, 安海忠, 高湘昀, 闻少博. 供给与需求驱动型原油价格变动对股票市场的多时间尺度影响研究[J]. 中国管理科学, 2018, 26(11): 62-73.
[8]	陈其安, 雷小燕. 货币政策、投资者情绪与中国股票市场波动性:理论与实证[J]. 中国管理科学, 2017, 25(11): 1-11.
[9]	闫红蕾, 赵胜民. 沪港通能否促进A股与香港股票市场一体化[J]. 中国管理科学, 2016, 24(11): 1-10.
[10]	熊正德, 文慧, 熊一鹏. 我国外汇市场与股票市场间波动溢出效应实证研究——基于小波多分辨的多元BEKK-GARCH(1,1)模型分析[J]. 中国管理科学, 2015, 23(4): 30-38.
[11]	谢海滨, 田军, 汪寿阳. 极端风险下中国股市的反应特征研究[J]. 中国管理科学, 2015, 23(11): 39-45.
[12]	王春. 投资者情绪对股票市场收益和波动的影响-基于开放式股票型基金资金净流入的实证研究[J]. 中国管理科学, 2014, 22(9): 49-56.
[13]	陈其安, 高国婷, 陈慧. 基于个人投资者过度自信的中国股票市场定价模型[J]. 中国管理科学, 2011, 19(4): 38-46.
[14]	翟爱梅, 周彤. 基于市场参与者行为假设的股票市场量价关系研究[J]. 中国管理科学, 2011, 19(4): 31-37.
[15]	林宇. 中国股市与国际股市的极值风险传导效应研究[J]. 中国管理科学, 2008, 16(4): 36-43.