Correlation Networks Among Currencies

By analyzing the foreign exchange market data of various currencies, we derive a hierarchical taxonomy of currencies constructing minimal-spanning trees. Clustered structure of the currencies and the key currency in each cluster are found. The clusters match nicely with the geographical regions of corresponding countries in the world such as Asia or East Europe, the key currencies are generally given by major economic countries as expected.Comment: 12 pages, 3 figures, 1 tabl

Lagged correlation networks

Technological advances have provided scientists with large high-dimensional datasets that describe the behaviors of complex systems: from the statistics of energy levels in complex quantum systems, to the time-dependent transcription of genes, to price fluctuations among assets in a financial market. In this environment, where it may be difficult to infer the joint distribution of the data, network science has flourished as a way to gain insight into the structure and organization of such systems by focusing on pairwise interactions. This work focuses on a particular setting, in which a system is described by multivariate time series data. We consider time-lagged correlations among elements in this system, in such a way that the measured interactions among elements are asymmetric. Finally, we allow these interactions to be characteristically weak, so that statistical uncertainties may be important to consider when inferring the structure of the system. We introduce a methodology for constructing statistically validated networks to describe such a system, extend the methodology to accommodate interactions with a periodic component, and show how consideration of bipartite community structures in these networks can aid in the construction of robust statistical models. An example of such a system is a financial market, in which high frequency returns data may be used to describe contagion, or the spreading of shocks in price among assets. These data provide the experimental testing ground for our methodology. We study NYSE data from both the present day and one decade ago, examine the time scales over which the validated lagged correlation networks exist, and relate differences in the topological properties of the networks to an increasing economic efficiency. We uncover daily periodicities in the validated interactions, and relate our findings to explanations of the Epps Effect, an empirical phenomenon of financial time series. We also study bipartite community structures in networks composed of market returns and news sentiment signals for 40 countries. We compare the degrees to which markets anticipate news, and news anticipate markets, and use the community structures to construct a recommender system for inputs to prediction models. Finally, we complement this work with novel investigations of the exogenous news items that may drive the financial system using topic models. This includes an analysis of how investors and the general public may interact with these news items using Internet search data, and how the diversity of stories in the news both responds to and influences market movements

Mining Novel Multivariate Relationships in Time Series Data Using Correlation Networks

In many domains, there is significant interest in capturing novel relationships between time series that represent activities recorded at different nodes of a highly complex system. In this paper, we introduce multipoles, a novel class of linear relationships between more than two time series. A multipole is a set of time series that have strong linear dependence among themselves, with the requirement that each time series makes a significant contribution to the linear dependence. We demonstrate that most interesting multipoles can be identified as cliques of negative correlations in a correlation network. Such cliques are typically rare in a real-world correlation network, which allows us to find almost all multipoles efficiently using a clique-enumeration approach. Using our proposed framework, we demonstrate the utility of multipoles in discovering new physical phenomena in two scientific domains: climate science and neuroscience. In particular, we discovered several multipole relationships that are reproducible in multiple other independent datasets and lead to novel domain insights.Comment: This is the accepted version of article submitted to IEEE Transactions on Knowledge and Data Engineering 201

Community detection in temporal multilayer networks, with an application to correlation networks

Networks are a convenient way to represent complex systems of interacting entities. Many networks contain "communities" of nodes that are more densely connected to each other than to nodes in the rest of the network. In this paper, we investigate the detection of communities in temporal networks represented as multilayer networks. As a focal example, we study time-dependent financial-asset correlation networks. We first argue that the use of the "modularity" quality function---which is defined by comparing edge weights in an observed network to expected edge weights in a "null network"---is application-dependent. We differentiate between "null networks" and "null models" in our discussion of modularity maximization, and we highlight that the same null network can correspond to different null models. We then investigate a multilayer modularity-maximization problem to identify communities in temporal networks. Our multilayer analysis only depends on the form of the maximization problem and not on the specific quality function that one chooses. We introduce a diagnostic to measure \emph{persistence} of community structure in a multilayer network partition. We prove several results that describe how the multilayer maximization problem measures a trade-off between static community structure within layers and larger values of persistence across layers. We also discuss some computational issues that the popular "Louvain" heuristic faces with temporal multilayer networks and suggest ways to mitigate them.Comment: 42 pages, many figures, final accepted version before typesettin