Department of Mathematics, King's College London, The Strand, London, WC2R 2LS, UK.
Department of Computer Science, University College London, Gower Street, London, WC1E 6BT, UK.
Sci Rep. 2014 Apr 4;4:4589. doi: 10.1038/srep04589.
We report evidence of a deep interplay between cross-correlations hierarchical properties and multifractality of New York Stock Exchange daily stock returns. The degree of multifractality displayed by different stocks is found to be positively correlated to their depth in the hierarchy of cross-correlations. We propose a dynamical model that reproduces this observation along with an array of other empirical properties. The structure of this model is such that the hierarchical structure of heterogeneous risks plays a crucial role in the time evolution of the correlation matrix, providing an interpretation to the mechanism behind the interplay between cross-correlation and multifractality in financial markets, where the degree of multifractality of stocks is associated to their hierarchical positioning in the cross-correlation structure. Empirical observations reported in this paper present a new perspective towards the merging of univariate multi scaling and multivariate cross-correlation properties of financial time series.
我们报告了纽约证券交易所每日股票收益的交叉相关性层次结构性质和多重分形性之间深度相互作用的证据。不同股票显示的多重分形程度与它们在交叉相关性层次结构中的深度呈正相关。我们提出了一个动力学模型，该模型再现了这一观察结果以及一系列其他经验性质。该模型的结构使得异质风险的层次结构在相关矩阵的时间演化中起着至关重要的作用，为金融市场中交叉相关性和多重分形性之间相互作用的机制提供了一种解释，其中股票的多重分形程度与其在交叉相关结构中的层次定位相关联。本文报告的实证观察为金融时间序列的单变量多标度和多变量交叉相关性性质的融合提供了一个新的视角。
