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。
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.
作者
谭政勋
黄锦东
叶诚
TAN Zheng-xun;HUANG Jing-dong;YE Cheng(Hunan Nornal University,College of Business,Changsha 410002,China;Jinan University,College of Economics,Guangzhou 510062,China)
出处
《中国管理科学》
CSSCI
CSCD
北大核心
2018年第12期12-24,共13页
Chinese Journal of Management Science
基金
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)
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
stock market
significant turning point
wavelet leader method
approximation technique
Bayesian estimation
