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

Abstract

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

CLC Number:

F830

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.

References

[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.

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

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10

[1]	TANG Zhen-peng, WU Jun-chuan, RAN Meng, ZHANG Ting-ting. Research on The Self-exciting Effect of Chinese Stock Market Considering Investor Sentiment [J]. Chinese Journal of Management Science, 2020, 28(7): 1-12.
[2]	XIE Chi, HU Xue-jing, WANG Gang-jin. Dynamic Evolution and Market Robustness of Chinese Stock Market in the Past 10 Years of the Financial Crisis: An Empirical Research Based on Complex Network Perspective [J]. Chinese Journal of Management Science, 2020, 28(6): 1-12.
[3]	CHEN Qi-an, ZHANG Hui, CHEN Shu-yu. Does Stock Index Futures Trading Increase the Stock Market Volatility in China?——Theoretical and Empirical Research Based on Investor Structure [J]. Chinese Journal of Management Science, 2020, 28(4): 1-13.
[4]	ZHANG Tong-hui, YUAN Ying, ZENG Wen. Can Investor Attention Help to Predict Stock Market Volatility? An Empirical Research Based on Chinese Stock Market High-frequency Data [J]. Chinese Journal of Management Science, 2020, 28(11): 192-205.
[5]	LIU Feng-gen, WU Jun-chuan, YANG Xi-te, OUYANG Zi-sheng. Long-run Dynamic Effect of Macro-economy on Stock Market Volatility Based on Mixed Frequency Data Model [J]. Chinese Journal of Management Science, 2020, 28(10): 65-76.
[6]	YIN Li-bo, WEI Ya, HAN Fu-ling. Study on Characteristics and Influence Factors of Time-varying Anomalies in China's Stock Market [J]. Chinese Journal of Management Science, 2019, 27(8): 14-25.
[7]	ZHAO Peng-ju, ZHANG Wei. Stock Market Evolution Research Based on Random Dynamic System [J]. Chinese Journal of Management Science, 2019, 27(5): 50-56.
[8]	YIN Hai-yuan, Zhu Xu. Investor Heterogeneous Beliefs, Expect Evolution and Stock Market Liquidity [J]. Chinese Journal of Management Science, 2019, 27(10): 12-21.
[9]	LUO Jia-wen, CHEN Lang-nan. The Volatility Co-movement of Various Stock Markets based on High-frequency Data [J]. Chinese Journal of Management Science, 2018, 26(2): 116-125.
[10]	XIA Ting, WEN Yue-chun. Does Economic Uncertainty Matter for Stock Market Volatility? An Analysis Based on GARCH-MIDAS [J]. Chinese Journal of Management Science, 2018, 26(12): 1-11.
[11]	WANG Zong-run, PAN Cheng-cheng. Research on the Evolution of Information Strategy and Herd Behavior based on Dynamic Scale-free Network [J]. Chinese Journal of Management Science, 2018, 26(12): 66-77.
[12]	WANG Qi-Zhen, WANG Yu-Dong. International Transmission of Volatility Among Crude Oil Prices, Economic Uncertainty and the Stock Market [J]. Chinese Journal of Management Science, 2018, 26(11): 50-61.
[13]	HUANG Shu-pei, AN Hai-zhong, GAO Xiang-yun, WEN Shao-bo. Multiscale Impacts of Oil Price Fluctuations Driven by the Demand and Supply on the Stock Market [J]. Chinese Journal of Management Science, 2018, 26(11): 62-73.
[14]	CHEN Qi-an, LEI Xiao-yan. Monetary Policy, Investor Sentiment and Volatility of Chinese Stock Market:Theory and Evidence [J]. Chinese Journal of Management Science, 2017, 25(11): 1-11.
[15]	CAO Dong, ZHANG Jia. The Impact of Index Future on Stock Market Volatility Based on the GARCH-M Model [J]. Chinese Journal of Management Science, 2017, 25(1): 27-34.