The relationship between currencies in foreign exchange markets has been a topic of significance in economics. Previous studies have focused more on correlations between currencies. However, the detection of causality can reveal their inherent laws. Although the traditional Granger causality test can identify causality, it cannot take into account the nature and intensity of the causality. Thus, the objective of this paper is to identify the causalities of currencies from the perspective of dynamics. In this paper, we select 25 currencies (with the US dollar (USD) as the numeraire) from foreign exchange markets, as they occupy large shares in their regions. To detect the causalities of the foreign exchange markets, we combine PC (pattern causality) theory and complex networks to construct directed and weighted causality networks, in which the nodes represent the currencies and the directed edges represent the causal intensities. Furthermore, we study the symmetry of each causality and quantify the symmetry degree. The results demonstrate that causalities exist between currencies that differ in terms of nature and intensity. The positive causality network exhibits substantial robustness, which can be regarded as the dominant causal relationship in the foreign exchange markets, although a few exceptions are encountered, such as the dominant negative and disordered causalities between currency pairs. In addition, the dominant causalities between most currencies are symmetric in terms of nature, and they also exhibit symmetry in terms of intensity. Furthermore, by gradually deleting the network by thresholding according to the edge weights, we identify the important driving currencies of the markets. This paper may provide valuable information for investors and supervisory departments.

中文翻译：

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外汇市场的多元因果推理

外汇市场中货币之间的关系一直是经济学中一个重要的话题。以前的研究更多地关注货币之间的相关性。但是，因果关系的检测可以揭示它们的内在规律。传统的格兰杰因果检验虽然可以识别因果关系，但不能考虑因果关系的性质和强度。因此，本文的目的是从动态的角度识别货币的因果关系。在本文中，我们从外汇市场中选择了 25 种货币（以美元 (USD) 作为计价单位），因为它们在其所在地区占有很大份额。为了检测外汇市场的因果关系，我们结合个人电脑（模式因果关系）理论和复杂网络来构建有向和加权因果网络，其中节点代表货币，有向边代表因果强度。此外，我们研究了每个因果关系的对称性并量化了对称程度。结果表明，在性质和强度方面不同的货币之间存在因果关系。正向因果网络表现出很强的稳健性，可以被视为外汇市场中的主导因果关系，但也有少数例外，例如货币对之间的主导负向和无序因果关系。此外，大多数货币之间的主导因果关系在性质上是对称的，在强度上也表现出对称性。此外，通过根据边缘权重进行阈值化逐渐删除网络，我们确定了市场的重要驱动货币。本文可为投资者和监管部门提供有价值的信息。