我国证券市场交互关系的多标度多重分形分析

Multiscale multifractal analysis on the cross-correlation of the China securities markets

股票市场、债券市场和基金市场作为金融市场的三个重要组成部分,市场间的相互关系受到投资者和管理者的广泛关注。本文选用我国上证综指、上证债指和上证基指的收益率序列为研究对象,运用多重分形去趋势波动分析法(MF-DFA)证实了三个市场的波动存在多重分形特征。同时,使用多标度多重分形去趋势交互相关分析法(MM-DCCA),在不同标度下,使用滑动窗技术,生成Hurst曲面可视化分析这三个市场中两两之间的交互相关性。实证结果表明,三个市场间的交互相关性在不同标度下呈现不同的分形特征;股票市场与基金市场的相关性强于其它两组市场的相关性,且股票市场与债券市场的相关性不稳定。

The stock market, the bond market and the fund market are three important components of financial markets, and the relationship among these three markets has been paid expansive attention by the investors and the managers. In this paper we choose the return series of Shanghai Composite Index, Bond Index and Fund Index as the research objects and use MF-DFA method to confirm the existence of multifractal features in the fluctuation of the three markets. Meanwhile, we utilize the MM- DCCA method at multiple scales and generate the Hurst surface to better visualize the interaction between markets respectively. The empirical results show that the cross-correlation among three markets presents various fractal characteristics at different scales. Besides, the correlation between the stock market and the fund market is stronger than that of the other two groups, and the correlation between the stock market and the bond market is unstable.