基于多重分形时间加权去趋势互相关分析及在股市互相关性分析中的应用

发布时间：2018-05-19 10:01

本文选题：互相关性 + 多重分形时间加权去趋势互相关分析(MF-TWXDFA)　；参考：《湘潭大学》2017年硕士论文

【摘要】：基于多重分形时间加权去趋势波动分析(MF-TWDFA)以及多重分形互相关分析(MFCCA),我们提出一种新的算法-多重分形时间加权去趋势互相关分析(MF-TWXDFA).该算法的创新在于估计局部趋势时采用地理加权回归模型的思想,计算去趋势协方差函数时考虑到波动函数的符号信息·我们将该算法与多重分形互相关分析(MFCCA)算法应用到仿真序列,以此来检验该算法的性能。数值模拟证明新算法可以准确地检测两个同时记录系列的长程互相关性。为了进一步展示多重分形时间加权去趋势互相关分析(MF-TWXDFA)算法的效用,我们将MF-TWXDFA应用于股票市场的时间序列,发现股票收益之间的幂律互相关具有明显的多重分形。同时,还定义了一个新的互相关系数-MF-TWXDFA互相关系数用于量化两个时间序列之间的互相关的水平。
[Abstract]:Based on multifractal time weighted detrend wave analysis (MF-TWDFA) and multifractal cross correlation analysis (MFCCA), a new algorithm - multifractal time weighted detrend cross correlation analysis (MF-TWXDFA) is proposed. The innovation of this algorithm lies in the thought of using the geographically weighted regression model to estimate the local trend and the calculation of the detrend Association. The difference function takes into account the symbolic information of the wave function. We apply the algorithm and the multifractal cross correlation analysis (MFCCA) algorithm to the simulation sequence to test the performance of the algorithm. The numerical simulation proves that the new algorithm can accurately detect the long range cross correlation of the two simultaneous recording series. In order to further display the multifractal, The utility of the weighted detrending cross correlation analysis (MF-TWXDFA) algorithm is applied to the time series of the stock market. We find that the power law cross correlation between stock returns has a distinct multifractal. At the same time, a new cross correlation coefficient -MF-TWXDFA correlation coefficient is also defined to be used to quantify the interaction between two time series. The related level.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F831.51;O189

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