The structure of the FX market can be modelled as a network, where each node represents an exchange rate between a pair of currencies, such as GBP/EUR or USD/CHN, and each edge reflects the strength of connection between two exchange rates. To infer the structure of this network, traditional methods in the literature compute the Pearson correlation between the evolution of pairs of exchange rate, and further construct a minimal spanning tree (MST) to capture the significant connections in the FX network. However, the mapping from the correlation to a distance measure is somewhat arbitrary, which leads to instability of the resulting MST; furthermore, the MST presents an overly simplified structure that might overlook important information in the FX network.
In this project, we apply state-of-the-art algorithms developed in the emerging field of graph signal processing (GSP) to infer dynamic network structure of the FX market of 69 currency pairs throughout different time periods. We demonstrate that, compared to the classical methods based on construction of MST from correlation matrix as well as the graphical Lasso, the GSP based method has its unique advantage in inferring FX network structure, due to its robustness against noise in the data as well as the induced smoothness that effectively filters out the redundant relations. Practically, the proposed method enables us to better evaluate the impact of recent international events, notably the Brexit referendum, the financial crisis in Russia, and the introduction of the Euro currency, on the global FX market.
Figure 1. Relationship between different currency pairs based on FX time series before, during, and after the introduction of Euro.