金融时间序列分形维参数估计方法比较及应用  

The Comparison and Application of Fractal Dimension Estimation Method for Financial Time Series

作　　者：许文坤[1] 张卫国[1] 

机构地区：[1]华南理工大学工商管理学院,广东广州510640

出　　处：《系统工程》2011年第7期11-18,共8页Systems Engineering

基　　金：教育部人文社会科学研究规划项目(07JA630048);国家杰出青年基金资助项目(70825005)

摘　　要：为了更精确地估计时间序列的Hurst指数值,本文通过引入Whittle算法,结合蒙特卡罗仿真实验,说明了Whittle算法克服了常用的R/S算法、修正R/S算法、V/S算法以及DFA等算法在精度和稳定性方面的缺陷。首先通过数值模拟,比较不同方法所得Hurst指数估计误差,验证了Whittle算法具有更高的精度和更好的稳定性。然后选用最好的估计算法并结合移动窗口技术对沪深市场的发展状态进行了实证应用,分析表明沪深市场近20年来的市场有效性更趋变强,收益率和波动率长记忆效应更趋变弱的结论。In this paper,we investigate a best Hurst estimation in order to improve the Hurst parameter estimation accuracy of time series.The Monte Carlo simulation shows that the Whittle method overcome the defects of precision and stability from R/S method,modify R/S method,V/S method,DFA method and other methods which are commonly used.Firstly,the numerical simulation is used to compare different methods of estimation error from Hurst parameter to verify that the Whittle method has higher precision and better stability.And then we use the best method with rolling window to analyze the development state of Shanghai and Shenzhen market.Empirical analysis shows that the long memory of returns and volatility are less persistent and the form of market efficiency hypothesis in Shanghai and Shenzhen is become stronger in the past 20 years.

关 键 词：分形布朗运动 Whittle算法 MR/S R/S V/S DFA 

分 类 号：F830[经济管理—金融学]