Date Published: February 8, 2018
Publisher: Public Library of Science
Author(s): Yong Kheng Goh, Haslifah M. Hasim, Chris G. Antonopoulos, Irene Sendiña-Nadal.
In this paper, we study data from financial markets, using the normalised Mutual Information Rate. We show how to use it to infer the underlying network structure of interrelations in the foreign currency exchange rates and stock indices of 15 currency areas. We first present the mathematical method and discuss its computational aspects, and apply it to artificial data from chaotic dynamics and to correlated normal-variates data. We then apply the method to infer the structure of the financial system from the time-series of currency exchange rates and stock indices. In particular, we study and reveal the interrelations among the various foreign currency exchange rates and stock indices in two separate networks, of which we also study their structural properties. Our results show that both inferred networks are small-world networks, sharing similar properties and having differences in terms of assortativity. Importantly, our work shows that global economies tend to connect with other economies world-wide, rather than creating small groups of local economies. Finally, the consistent interrelations depicted among the 15 currency areas are further supported by a discussion from the viewpoint of economics.
In finance, researchers use complex systems theory to understand the behaviour and dynamics of financial markets, as they can be regarded as complex systems with large numbers of interacting financial agents . Treating financial markets as a complex system helps in understanding their relationship to other complex systems and using common approaches to study them. The interactions among the constituent parts in such systems are frequently non-linear.
We first tested the method by attempting to reproduce the structure of known networks where the dynamics in their nodes is given by chaotic maps, before applying it to data from financial markets. Particularly, we start with networks with given binary adjacency matrices (which we call original adjacency matrices) to allow for comparisons between the original and the inferred one. By binary, we mean two nodes in the network can either be directly connected, which corresponds to an entry equal to 1 in the matrix, or unconnected, which corresponds to a 0 entry. Moreover, since the connections are considered bidirectional, the adjacency matrices will be symmetric. We then couple the chaotic maps according to the original adjacency matrices and record the evolution of their dynamics and produce time-series data for each node in the original network. Next, we input these time-series data to the proposed method, which produces an inferred, binary adjacency matrix. To quantify the percentage of successful inference, we subtract the original from the inferred adjacency matrix. If the resulting matrix is the zero matrix, then we call this 100% successful network inference. Should there be spurious or missed connections, this difference would not be the zero matrix, and thus would correspond to a smaller percentage. For example, 100% successful inference means that the proposed method infers correctly all connections in the original network used to produce the recorded data, with no spurious or missed connections.
So far, we have demonstrated the applicability of the method to infer successfully the network structure for artificial data, and we now use it to infer the connectivity in networks of financial-markets data.
In this paper, we used the normalised Mutual Information Rate to infer the network structure in artificial and financial-markets data of 15 currency areas including the EU, from 2000 to 2016. Specifically, we showed how the underlying network connectivity among the nodes of financial time-series data, such as foreign currency exchange-rates and stock-indices can be inferred. We first demonstrated the applicability of the method by applying it to artificial data from chaotic dynamics and to cases of correlated normal variates. Our results for the artificial data showed that the method can be used to successfully infer the underlying network structures. This uses the data recorded from the coupled dynamics and assumes no previous knowledge of the adjacency matrices, other than to estimate the percentage of successful network inference.