基于分形分析的我国股市波动性研究
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摘要
本文以上证综指和深成指收益率为研究对象，试图在对它们的分形特征进行分析的基础上，以股市的长记忆性为基础，即以股市非有效为前提，对我国股市收益率的波动特征和宏观经济影响因素进行系统分析，以期为投资者的理性投资和国家的宏观金融调控提供理论参考。
首先，本文对基于标度对称性理论的一类分形参数估计方法进行改进，提出综合利用多种分形分析方法对我国股市收益率进行分形分析的思路。综合利用DFA、滑动窗DFA、R／S分析和改进的分形参数估计方法对我国股市收益率序列和波动序列进行单分形分析，结果显示我国股市收益率序列和波动序列均具有长记忆特征，说明我国股市为非有效市场。在此基础上，进一步综合利用滑动窗MFDFA和WTMM方法对我国股市收益率的多重分形特征进行分析，验证了股市多重分形结构的存在。
其次，在股市存在双长记忆性的前提下，引入残差服从偏t分布的ARFIMA-FIAPARCH和ARFIMA-HYG ARCH模型，对沪深股市收益率序列进行了计量分析，结果显示我国股市收益率存在显著的聚集性和杠杆效应，且在1996年前后有增强趋势。而且，从VaR估计的角度，分析了对长记忆性、聚集性和杠杆效应具有较强刻画能力的ARFIMA-FIAPARCH-skt和ARFIMA-HYGARCH-skt模型对我国股市收益率的短期预测效果。
接着，利用长记忆VAR-BEKK-MVGARCH模型以及去除长记忆性序列的Granger因果检验，对沪深股市收益率之间的均值溢出效应和波动溢出效应进行了检验，结果表明：整个1991-2006年期间沪深股市收益率的均值溢出效应不显著，且仅具有单向波动溢出效应；但2000年以后的沪深股市收益率均显示出较显著的双向均值溢出效应和双向波动溢出效应。另外，DCC检验表明沪深股市收益率间具有一定程度的动态相关性。
再次，以股市收益率的均值溢出效应为基础，通过构建VAR系统来考察宏观经济因素对我国股市收益率的影响。结果显示：在短期水平上，包括利率、货币供应量和汇率在内的货币政策对我国股市具有重要影响；在长期水平上，我国股市收益率与实体经济间具有显著的相关性。
Returns of Shanghai Synthesis index and Shenzhen Composition index are taken as the studyobject. By analyzing their fractals foundation, we are attempting to carry on the systematicanalysis of the fluctuation characteristic of our country's stock market returns and the macroscopiceconomical influence, taking stock market's long memory as the foundation, namely taking thenon-effective of stock market as the premise to provide the theoretical reference for investors'rational investment and the national macroscopic financial regulation.
First, a kind of method on estimating the fractal parameter in scaling symmetrical theory isimproved, and the fractal analysis of stock market returns of our country is proposed by thecomprehensive utilization of many kinds of fractal analyze methods. We carried out the list fractalanalysis of stock market returns of our country series and the fluctuation series by using DFA,sliding windows DFA, R/S analysis and the improved fractal parameter estimation method. Thefindings demonstrate stock market returns of our country series and the fluctuation series have thelong memory characteristic, which means that the stock market of our country is the non-effectivemarket. Based on the findings mentioned above, further analysis of the multifractal characteristicsof our country's stock market returns was made by using sliding windows MFDFA and theWTMM method, which confirms the existence of multifractal structure in our country's stockmarket.
Next, we have carried out the measurement analysis of the Shanghai and Shenzhen stockmarket returns series by using the ARFIMA-FIAPARCH model. ARFIMA-HYGARCH modeland skew t distribution, taking the existence of the dual long memory in the stock market aspremise. The result shows that the volatility clustering and the leverage effect do exist in ourcountry's stock market returns, and had the tendency of enhancement in around 1996. At the sametime we have analyzed, from the VaR estimation angle, the forecast effect of theARFIMA-FIAPARCH-skt model and ARFIMA- HYGARCH-skt model what has the strongportray ability to long memory, the volatility clustering and the leverage effect to stock marketreturns of our country.
Then, we examined the mean spillover effect and the volatility spillover effect betweenShanghai and Shenzhen returns stock market with the help of the VAR-BEKK-MVGARCH model and the Granger causality test which is to remove the long memory series, and find that the meanspillover effect in Shanghai and Shenzhen stock market returns from 1991 to 2006 was notobvious, and that there was only the unidirectional volatility spillover effect. But the bidirectionalmean spillover effect and the bidirectional volatility spillover effect in Shanghai and Shenzhenstock market returns has been more obvious since 2000. Moreover, the DCC test indicated therewas, to some degree, dynamic correlation between the Shanghai and Shenzhen stock marketreturns.
Last, we tried to inspect the influence of the macroscopic economy on the ratio of ourcountry's stock market returns by constructing the VAR system on the basis of the mean spilloereffect in returns stock market. The result demonstrate that in the short run, the monetary policy,including the rate, the money supply and the exchange rate, has great influence on the stockmarket of our country, while in the long run, there is obvious correlation between our country'sstock market returns and the entity economy.
首先，本文对基于标度对称性理论的一类分形参数估计方法进行改进，提出综合利用多种分形分析方法对我国股市收益率进行分形分析的思路。综合利用DFA、滑动窗DFA、R／S分析和改进的分形参数估计方法对我国股市收益率序列和波动序列进行单分形分析，结果显示我国股市收益率序列和波动序列均具有长记忆特征，说明我国股市为非有效市场。在此基础上，进一步综合利用滑动窗MFDFA和WTMM方法对我国股市收益率的多重分形特征进行分析，验证了股市多重分形结构的存在。
其次，在股市存在双长记忆性的前提下，引入残差服从偏t分布的ARFIMA-FIAPARCH和ARFIMA-HYG ARCH模型，对沪深股市收益率序列进行了计量分析，结果显示我国股市收益率存在显著的聚集性和杠杆效应，且在1996年前后有增强趋势。而且，从VaR估计的角度，分析了对长记忆性、聚集性和杠杆效应具有较强刻画能力的ARFIMA-FIAPARCH-skt和ARFIMA-HYGARCH-skt模型对我国股市收益率的短期预测效果。
接着，利用长记忆VAR-BEKK-MVGARCH模型以及去除长记忆性序列的Granger因果检验，对沪深股市收益率之间的均值溢出效应和波动溢出效应进行了检验，结果表明：整个1991-2006年期间沪深股市收益率的均值溢出效应不显著，且仅具有单向波动溢出效应；但2000年以后的沪深股市收益率均显示出较显著的双向均值溢出效应和双向波动溢出效应。另外，DCC检验表明沪深股市收益率间具有一定程度的动态相关性。
再次，以股市收益率的均值溢出效应为基础，通过构建VAR系统来考察宏观经济因素对我国股市收益率的影响。结果显示：在短期水平上，包括利率、货币供应量和汇率在内的货币政策对我国股市具有重要影响；在长期水平上，我国股市收益率与实体经济间具有显著的相关性。
Returns of Shanghai Synthesis index and Shenzhen Composition index are taken as the studyobject. By analyzing their fractals foundation, we are attempting to carry on the systematicanalysis of the fluctuation characteristic of our country's stock market returns and the macroscopiceconomical influence, taking stock market's long memory as the foundation, namely taking thenon-effective of stock market as the premise to provide the theoretical reference for investors'rational investment and the national macroscopic financial regulation.
First, a kind of method on estimating the fractal parameter in scaling symmetrical theory isimproved, and the fractal analysis of stock market returns of our country is proposed by thecomprehensive utilization of many kinds of fractal analyze methods. We carried out the list fractalanalysis of stock market returns of our country series and the fluctuation series by using DFA,sliding windows DFA, R/S analysis and the improved fractal parameter estimation method. Thefindings demonstrate stock market returns of our country series and the fluctuation series have thelong memory characteristic, which means that the stock market of our country is the non-effectivemarket. Based on the findings mentioned above, further analysis of the multifractal characteristicsof our country's stock market returns was made by using sliding windows MFDFA and theWTMM method, which confirms the existence of multifractal structure in our country's stockmarket.
Next, we have carried out the measurement analysis of the Shanghai and Shenzhen stockmarket returns series by using the ARFIMA-FIAPARCH model. ARFIMA-HYGARCH modeland skew t distribution, taking the existence of the dual long memory in the stock market aspremise. The result shows that the volatility clustering and the leverage effect do exist in ourcountry's stock market returns, and had the tendency of enhancement in around 1996. At the sametime we have analyzed, from the VaR estimation angle, the forecast effect of theARFIMA-FIAPARCH-skt model and ARFIMA- HYGARCH-skt model what has the strongportray ability to long memory, the volatility clustering and the leverage effect to stock marketreturns of our country.
Then, we examined the mean spillover effect and the volatility spillover effect betweenShanghai and Shenzhen returns stock market with the help of the VAR-BEKK-MVGARCH model and the Granger causality test which is to remove the long memory series, and find that the meanspillover effect in Shanghai and Shenzhen stock market returns from 1991 to 2006 was notobvious, and that there was only the unidirectional volatility spillover effect. But the bidirectionalmean spillover effect and the bidirectional volatility spillover effect in Shanghai and Shenzhenstock market returns has been more obvious since 2000. Moreover, the DCC test indicated therewas, to some degree, dynamic correlation between the Shanghai and Shenzhen stock marketreturns.
Last, we tried to inspect the influence of the macroscopic economy on the ratio of ourcountry's stock market returns by constructing the VAR system on the basis of the mean spilloereffect in returns stock market. The result demonstrate that in the short run, the monetary policy,including the rate, the money supply and the exchange rate, has great influence on the stockmarket of our country, while in the long run, there is obvious correlation between our country'sstock market returns and the entity economy.
引文
① 可参见张世英，樊智．协整理论与波动模型：金融时间序列分析及应用[M]．北京：清华大学出版社，2004．
① 这篇文章是转引，出处为：Farmer j. D.. Santa Fe Institute Working Paper 98-12-17．
② 这篇文章是转引，出处为：Jefferies P, Hart M. L., Hui P. M., Johnson N. F. Eur. Phys. J. B, 2001, 20:493.
③ 这里的广义Hurst指数方法不同于上面的MFDFA方法，参见Norouzzadeh & Jafari(2005)
① 关于此类模型的具体介绍可参见：张世英，樊智．协整理论与波动模型[M]．北京：清华大学出版社，2004．
① 因为1991年5月4日为周六，故上证综合指数事实上是从1991年5月6日开始。
① 此数字为估计值，因为Eviews5.0估计的滞后阶数为750，此时F统计量的值为2.5691。
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① 这篇文章是转引，出处为：Farmer j. D.. Santa Fe Institute Working Paper 98-12-17．
② 这篇文章是转引，出处为：Jefferies P, Hart M. L., Hui P. M., Johnson N. F. Eur. Phys. J. B, 2001, 20:493.
③ 这里的广义Hurst指数方法不同于上面的MFDFA方法，参见Norouzzadeh & Jafari(2005)
① 关于此类模型的具体介绍可参见：张世英，樊智．协整理论与波动模型[M]．北京：清华大学出版社，2004．
① 因为1991年5月4日为周六，故上证综合指数事实上是从1991年5月6日开始。
① 此数字为估计值，因为Eviews5.0估计的滞后阶数为750，此时F统计量的值为2.5691。
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