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arXiv 0810.1215q-fin.STphysics.soc-ph
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世界货币交换网络中的无标度效应

Scale free effects in world currency exchange network

A. Z. Gorski, S. Drozdz, J. Kwapien

摘要:

大量收集的每日时间序列的60种世界货币的汇率被认为是。计算相关矩阵,并为这些货币中的每一种构建相应的最小生成树(MST)图,用作剩余货币的参考。结果表明,MST图的节点的多重性,以一个很好的近似开发一个类似的权力,标度指数类似的其他几个复杂的系统研究到目前为止,无标度分布。此外,有利于世界货币兑换网络的层次组织的定量参数提供了有关的结构,上述MST图和它们的标度指数,从一个完全可解的层次网络模型。在所考虑的时期内,美元的特殊地位可以归因于MST特征的一些偏离,当这种货币(或与之相关的其他货币)用作参考时,从典型的节点分层聚类特征到对应于随机图的特征。尽管一般来说,MST的基本结构在改变参考货币方面是稳健的,但当相关性增加时,可以观察到从有点分散(如美元的情况)到更紧凑的MST拓扑结构的系统性过渡的一些痕迹。

英文摘要:

A large collection of daily time series for 60 world currencies' exchange rates is considered. The correlation matrices are calculated and the corresponding Minimal Spanning Tree (MST) graphs are constructed for each of those currencies used as reference for the remaining ones. It is shown that multiplicity of the MST graphs' nodes to a good approximation develops a power like, scale free distribution with the scaling exponent similar as for several other complex systems studied so far. Furthermore, quantitative arguments in favor of the hierarchical organization of the world currency exchange network are provided by relating the structure of the above MST graphs and their scaling exponents to those that are derived from an exactly solvable hierarchical network model. A special status of the USD during the period considered can be attributed to some departures of the MST features, when this currency (or some other tied to it) is used as reference, from characteristics typical to such a hierarchical clustering of nodes towards those that correspond to the random graphs. Even though in general the basic structure of the MST is robust with respect to changing the reference currency some trace of a systematic transition from somewhat dispersed -- like the USD case -- towards more compact MST topology can be observed when correlations increase.

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