[论文解读] Stock market comovements: nonlinear approach for 48 countries

Paulo Ferreira, Andreia Dionísio+1 more|arXiv (Cornell University)|Feb 1, 2015

Complex Systems and Time Series Analysis被引用 3

一句话总结

本研究利用线性方法（协整、格兰杰因果关系）与非线性方法（互信息、MF-DFA、MF-DXA），分析了48个国家股票市场的联动性，揭示了新兴市场与前沿市场之间存在强烈的非线性依赖关系。研究证实所有配对均存在多重分形交叉相关性，且在负矩时刻显著偏离线性关系，并通过$σ_{DCCA}$量化了持续的交叉相关性。结果表明，全球权益市场联动性主要受非线性动力学与多重分形结构主导。

ABSTRACT

This paper examines the stock market comovements using basically three different approaches. Firstly, we used the most common linear analysis, based on cointegration and Granger causality tests; secondly we applied a nonlinear approach, using mutual information to analyze nonlinear dependence. Since underlying data sets are affected by non-stationarities, we also applied MF-DFA and MF-DXA in order to examine the multifractality nature of data and to analyze the relationship and mutual interaction between pairs of series, respectively. The overall results are quite interesting, since we found only 170 pair of stock markets cointegrated, and according to the Granger causality and mutual information we realized that the strongest relations lies between emerging markets, and between emerging and frontier markets. According to scaling exponent given by MF-DFA, $h(q=2)>1$, we found that all underlying data belong to non-stationary process. There is no cross-over in the fluctuation functions determined by MF-DFA method confirmed that mentioned approach could remove trends embedded in the data sets. The nature of cross-correlation exponent based on Mf-DXA is almost multifractal for all stock market pairs. The empirical relation, $h_{xy}(q)=[h_{xx}(q)+h_{yy}(q)]/2$ was confirmed just for $q>0$, while for $q<0$ there was a deviation from this relation. Width of singularity spectrum is in the range $\Delta \alpha_{xx}\in [0.304,0.905]$ which is another confirmation about multifractality nature of underlying data sets. The singularity spectrum for cross-correlation is in the range $\Delta \alpha_{xy}\in [0.246,1.178]$ confirming more complex relation between stock markets. The value of $\sigma_{DCCA}$ which is a measure for quantifying degree of cross-correlation indicates that all stock market pairs in the underlying time interval belong to cross-correlated series.

研究动机与目标

• 探究全球股票市场联动性的程度与本质，超越线性依赖关系。
• 利用先进的标度技术评估个体市场时间序列与交叉相关市场时间序列中的多重分形性。
• 评估线性关系（协整、格兰杰因果关系）对互信息与交叉相关性分析所捕捉的非线性依赖关系的稳健性。
• 通过$σ_{DCCA}$与奇异性谱量化股票市场配对之间的交叉相关性程度与结构。

提出的方法

• 采用线性协整与格兰杰因果关系检验，检测股票市场指数之间的长期均衡与预测关系。
• 应用互信息检测线性方法无法捕捉的非线性依赖结构。
• 使用多重分形去趋势波动分析（MF-DFA）评估个体市场收益率序列的多重分形特性，其中$h(q=2) > 1$ 表明非平稳性。
• 应用多重分形去趋势交叉相关分析（MF-DXA）研究市场配对之间的交叉相关性，估计$h_{xy}(q)$ 与奇异性谱。
• 计算交叉相关性程度度量$σ_{DCCA}$，以量化所有配对之间的交叉相关性强度。
• 验证$q > 0$时的经验关系$h_{xy}(q) = [h_{xx}(q) + h_{yy}(q)]/2$，并分析$q < 0$时的偏离情况。

实验结果

研究问题

• RQ1 协整与格兰杰因果关系等线性方法在检测全球股票市场有意义联动性方面有多大的有效性？
• RQ2 作为非线性依赖的度量，互信息所揭示的依赖关系与线性关系相比，在解释市场联动性方面有何差异？
• RQ3 个体股票市场收益率序列的多重分形程度如何？其在不同国家之间有何差异？
• RQ4 市场配对之间的交叉相关性结构与线性预期有何不同，特别是在不同矩（$q$）下？
• RQ5 所观测到的交叉相关性在所有48个国别配对中具有多大程度的持续性与可量化性？

主要发现

• 在所有可能的股票市场配对中，仅有170对被发现存在协整关系，表明长期均衡关系有限。
• 互信息与格兰杰因果关系结果表明，新兴市场与前沿市场之间的依赖关系最强，凸显了非线性依存性。
• 标度指数$h(q=2) > 1$ 确认了所有个体市场收益率序列均为非平稳性，支持了去趋势化方法的使用。
• MF-DFA波动函数中无交叉点的存在表明，该方法有效去除了数据中的趋势。
• 个体市场的奇异性谱宽度$Δ\alpha_{xx} \in [0.304, 0.905]$ 确认了所有收益率序列中均存在多重分形性。
• $σ_{DCCA}$值表明所有股票市场配对均存在交叉相关性，且交叉相关谱$Δ\alpha_{xy} \in [0.246, 1.178]$ 显示其复杂性高于个体序列。