Phase Synchronization based Minimum Spanning Trees for the Analysis and Visualization of Currency Exchange Markets

Correlation based Minimum Spanning Tree (MST) networks are instrumental in capturing the basic workings of a system and have been accepted for use in the analysis of stock and currency exchange markets. Research in network analysis of financial markets shows that although correlations underlying MST networks capture essential information, they do not faithfully capture dynamic behavior embedded in the time series data of financial systems. We present a new Phase Synchronization (PS) based method for establishing correlations between nonlinear time series data, prior to constructing the MST. In this method, time series data generated by each entity in a system is transformed to a recurrence plot and the recurrence plots are further transformed to trajectories in phase space. For each pair of trajectories, phase synchronization (PS) is quantified based on the degree of phase locking observed. Distances for the MST are then computed as a function of the PS between each entity pair. We demonstrate the method using Thailand Baht exchange rates with 82 countries from 2004 to 2012. We further analyze and compare networks constructed using the PS method (PS-MST) and the existing cross-correlation method (CC-MST), to study the differences in market dynamics captured by these methods.