In this paper, we seek to examine the relationship and dynamic dependence structure between the Australian dollar (AUD), euro (EUR), and the British pound (GBP), expressed in American dollars (USD) using a multivariate fractional cointegration model. Our empirical analysis reveals several important findings. First, the main advantage of this approach is to detect the long-term relationship as well as the short-term dynamics and to represent the interdependence between the variables. We further estimate a multivariate GARCH type model that enables us to examine the dynamic conditional correlations (short-run links) among the considered variables under the effects of long-run interactions and volatility persistence. We determine that the volatility transmission was time-varying and that influence from the crisis. Moreover, the joint distribution is explored using the Gumbel copulas in order to describe the nonlinear structure of dependence between the variables. The empirical results provide evidence of fractional cointegration between the exchanges rates and show long-run causal links between the variables and we find significant bidirectional causal links. In particular, we show a positive dynamic correlation and the dependence structure is represented by the optimal copula coefficient used for measuring the risk spillovers between the exchange rates.

在本文中，我们试图使用多元分数协整模型研究以美元 (USD) 表示的澳元 (AUD)、欧元 (EUR) 和英镑 (GBP) 之间的关系和动态依赖结构。我们的实证分析揭示了几个重要的发现。首先，这种方法的主要优点是检测长期关系以及短期动态，并表示变量之间的相互依赖性。我们进一步估计了一个多变量 GARCH 类型模型，该模型使我们能够在长期相互作用和波动持久性的影响下检查所考虑变量之间的动态条件相关性（短期联系）。我们确定波动率传递是随时间变化的，并且受到危机的影响。而且，使用 Gumbel copula 探索联合分布，以描述变量之间依赖关系的非线性结构。实证结果提供了汇率之间部分协整的证据，并显示了变量之间的长期因果关系，我们发现了重要的双向因果关系。特别是，我们显示了正动态相关性，并且依赖结构由用于衡量汇率之间风险溢出的最佳 copula 系数表示。