【作者】 陈曦；

【导师】 周炜星；

【作者基本信息】 华东理工大学 ， 应用经济学， 2011， 硕士

【摘要】 本文以2000年1月1日至2008年3月31日在沪市交易的所有880只A股股票的1分钟收盘数据为研究对象,引入截面收益率的概念,对两个主要变量——1分钟股票价格截面收益率及其波动率的概率分布、长期记忆性和多重分形特征进行研究。实证研究表明,1分钟股票价格截面收益率服从T分布,特征指数ζ3.1538；1分钟截面收益波动率存在“L”形日内效应,它的概率分布与互补累计概率分布均服从幂律分布,但幂指数不符合负三次方定律。通过降趋脉动分析法对1分钟股票价格收益率及其波动率的时间相关性进行研究,发现1分钟截面收益率的赫斯特指数值接近0.5,呈随机游走状态,不具有长期记忆性；而1分钟截面收益波动率的赫斯特指数接近于1,具有很强的长期记忆性。本文还运用多重分形降趋脉动分析法和数盒子法分别对1分钟股票价格截面收益率及其波动率的多重分形特征进行研究,发现1分钟截面收益率的多重分形标度指数τ(q)为非线性函数,其奇异性强度指数α≠1,且Δα远大于0,说明1分钟股票价格截面收益率具有多重分形特征；而1分钟截面收益波动率的多重分形标度指数τ(q)为线性函数,且τ(q)=q-1,其奇异性强度指数α≈1,且Δa接近于0,说明1分钟股票价格截面收益波动率不具有多重分形特征。更多还原

【Abstract】 We study the probability distribution, long memory and multi-fracial properties of two important variables, which are the ensemble return and the ensemble volatility of one minute stock close price, using the high-frequency data of all the A stocks’one minute close price from 2000.01.01 to 2008.03.31 in Shanghai stock market. We find that the probability distribution of one minute ensemble return meet the Student’s distribution, with its characteristic exponentζ= 3.1538, obeying the inverse cubic law. And we also find that one minute ensemble volatility has intraday effect with "L" shape intraday pattern, its probability distribution and complementary probability distribution are both meet the power-law distribution, but their exponents don’t obey the inverse cubic law. We study the long memory of one minute ensemble return using Detrended fluctuation analysis method with the result show that its Hurst index close to 0.5, which indicate that one minute ensemble return follow random work, and doesn’t have long memory. On the other hand, the Hurst index of one minute ensemble volatility is close to 1, which indicates one minute ensemble volatility has long memory. We respectively study the multiracial characterize of one minute ensemble return and its volatility with Multiracial detrended fluctuation analysis method and Box-counting method, and find that the multiracial scaling exponentτ(q) of one minute ensemble return is a nonlinear function, the singularity strength exponentαdoesn’t equal to 1, and△αis much larger than 0, which indicate that one minute ensemble return has multiracial characterize; otherwise, the multiracial scaling exponentτ(q) of one minute ensemble volatility is a linear function, its singularity strength exponent a is close to 1, and△αis close to 0, which indicate that one minute ensemble return doesn’t have multiracial characterize.更多还原