基于DFA的股市极端波动率阈值的确定及应用——基于系统动力学视角
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摘要
如何科学合理地界定极端波动的阈值是研究金融极端事件最为关键和核心的问题,而目前该方面的研究十分有限,且传统的方法(如标准差法和百分位法等)都存在较强的经验性和主观性。本文基于系统动力学这一研究视角,尝试用一种新的复杂性方法来解决这一问题。由于金融市场极端波动事件是金融市场演化的极端状态或受到外界扰动而导致的异常状态。而金融市场的长程相关性不受或很少受极端状态的影响,因此可以运用DFA(消除趋势波动分析)方法,通过确定序列的DFA指数何时开始收敛于原始值来确定极端波动率阈值。本文以上证指数为研究样本,运用DFA方法对股市极端波动率进行定量化研究:首先,对股市波动率的长程时间关联进行分析,发现上海股票市场存在着固有的长期持续性的演化状态;其次,运用基于DFA的极端事件阈值确定方法确定了上海股市极端波动率的阈值,进而运用Du等提出的严重度指数对股市极端波动事件发生的严重度进行实证分析,结果发现上述研究方法在研究股市极端波动方面具有较好的应用效果。
The most critical and essential issue of study of financial market extreme events is how to define threshold of extreme events scientifically and rationally.As extreme fluctuation of financial market is the extreme state of financial market evolution,or the abnormal state caused by external disturbances,while the long range correlation of financial market is not or rarely affected by extreme conditions,DFA(Detrended Fluctuation Analysis)method can be used to determine extreme volatility threshold by determining when the DFA index of the sequence starts to converge to the original value.From the perspective of complexity science,using the most typical index of Chinese stock market,Shanghai Composite Index,this paper conducts quantitative research on the extreme volatility of Chinese stock market using DFA method.Firstly,the long range time correlation of stock market volatility is analyzed,it is found that Shanghai stock market has an inherently long-term continuous evolution state.Secondly,the extreme volatility threshold of Shanghai stock market is determined using DFA-based extreme event threshold determination method,and then the annual severity index of stock market extreme fluctuation is measured,it is indicated that the research method above has a good application effect in studying stock market extreme fluctuation.In order to further test the effectiveness of the method above,the DFA method and traditional percentile method are compared,proving the superiority of DFA method.
The most critical and essential issue of study of financial market extreme events is how to define threshold of extreme events scientifically and rationally.As extreme fluctuation of financial market is the extreme state of financial market evolution,or the abnormal state caused by external disturbances,while the long range correlation of financial market is not or rarely affected by extreme conditions,DFA(Detrended Fluctuation Analysis)method can be used to determine extreme volatility threshold by determining when the DFA index of the sequence starts to converge to the original value.From the perspective of complexity science,using the most typical index of Chinese stock market,Shanghai Composite Index,this paper conducts quantitative research on the extreme volatility of Chinese stock market using DFA method.Firstly,the long range time correlation of stock market volatility is analyzed,it is found that Shanghai stock market has an inherently long-term continuous evolution state.Secondly,the extreme volatility threshold of Shanghai stock market is determined using DFA-based extreme event threshold determination method,and then the annual severity index of stock market extreme fluctuation is measured,it is indicated that the research method above has a good application effect in studying stock market extreme fluctuation.In order to further test the effectiveness of the method above,the DFA method and traditional percentile method are compared,proving the superiority of DFA method.
引文
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[14]苑莹,庄新田,金秀.中国股市的日内效应、长记忆性及多重分形性:基于价-量交叉相关性视角[J].2016,25(1):28-35.
[15]CHEN H P,SUN X,WU Z Q,et al.Enlightenment from various conditional probabilities about Hang Seng index in Hong Kong stock market[J].Physica A,2004,335(1/2):183-196.
[2]FORM O S.The implications of the global financial crisis for low-income countries[J].International Monetary Fund,2009,3(1):234-287.
[3]DONG J,LIU X Q,HUANG L X.The influence and inspiration of American subprime mortgage crisis on Chinese economy[J].Sci-Tech Information Development&Economy,2008,26(56):45-78.
[4]TIM B,RAY Y C,KENNETH F K.ARCH modeling in finance:A review of the theory and empirical evidence[J].Journal of Econometrics,1992,52(1/2):50-59.
[5]ANDREW-KAROLYI G.A multivariate GARCHmodel of international transmissions of stock returns and volatility:The case of the United States and Canada[J].Journal of Business&Economic Statistics,1995,13(1):11-25.
[6]MALKIEL B G,FAMA E F.Efficient capital markets:A review of theory and empirical work[J].The Journal of Finance,1970,25(2):383-417.
[7]LAFFONT J J,MASKIN E S.The efficient market gypothesis and insider trading on the stock market[J].Journal of Political Economy,1990,98(1):70-93.
[8]IKEDA Y,TOKINAGA S.Multi-fractality analysis of artificial stock prices generated by behaviors of multi-agents using GP learning and its applications to recognition of factors governing prices[J].Ieice Technical Report Speech,2007(107):7-12.
[9]苏治,方明,李志刚.STAR与ANN模型:证券价格非线性动态特征及可预测性研究[J].中国管理科学,2008,16(5):9-16.
[10]CHUANG W I,HUANG T C,LIN B H.Predicting volatility using the Markov-switching multifractal model:Evidence from S&P 100index and equity options[J].North American Journal of Economics&Finance,2013,25(C):168-187.
[11]GUNAY S.Performance of the multifractal model of asset returns(MMAR):Evidence from emerging stock markets[J].International Journal of Financial Studies,2016,4(2):1-17.
[12]SCORNETTE D,ZHOU W X.Predictability of large future changes in major financial indices[J]International Journal of Forecasting,2006,22(1):153-168.
[13]魏宇,黄登仕.金融市场的多标度分形现象及其风险管理的关系[J].管理科学学报,2003,6(1):87-91.
[14]苑莹,庄新田,金秀.中国股市的日内效应、长记忆性及多重分形性:基于价-量交叉相关性视角[J].2016,25(1):28-35.
[15]CHEN H P,SUN X,WU Z Q,et al.Enlightenment from various conditional probabilities about Hang Seng index in Hong Kong stock market[J].Physica A,2004,335(1/2):183-196.