Identifying universal behavior is a challenging task for far-from-equilibrium complex systems. Here we investigate the collective dynamics of the international currency exchange market and show the existence of a semi-invariant signature  masked by the high degree of heterogeneity in this complex system. The cumulative fluctuation distribution in the exchange rates of different currencies possess heavy tails characterized by exponents varying around a median value of 2. The systematic deviation of individual currencies from this putative universal form (the "inverse square law" ) can be partly ascribed to the differences in their economic prosperity and diversity of export products. The distinct nature of the fluctuation dynamics for currencies of developed , emerging and frontier economiesare characterized in detail by detrended fluctuation analysis and variance-ratio tests, which shows that less developed economies are associated with sub-diffusive random walk processes . We hierarchically cluster the currencies into similarity groups based on differences between their fluctuation distributions as measured by Jensen-Shannon divergence. These clusters are consistent with the nature of the underlying economies - but also show striking divergences during economic crises. Indeed a temporally resolved analysis of the fluctuations indicates significant disruption during the crisis of 2008-09 underlining its severity .
Identifying behavior that is relatively invariant under different conditions is a challenging task in far-from-equilibrium complex systems. As an example of how the existence of a semi-invariant signature can be masked by the heterogeneity in the properties of the components comprising such systems, we consider the exchange rate dynamics in the international currency market. We show that the exponents characterizing the heavy tails of fluctuation distributions for different currencies systematically diverge from a putative universal form associated with the median value (~2) of the exponents. We relate the degree of deviation of a particular currency from such an "inverse square law" to fundamental macroscopic properties of the corresponding economy, viz., measures of per capita production output and diversity of export products. We also show that in contrast to uncorrelated random walks exhibited by the exchange rate dynamics for currencies belonging to developed economies, those of the less developed economies show characteristics of sub-diffusive processes which we relate to the anti-correlated nature of the corresponding fluctuations. Approaches similar to that presented here may help in identifying invariant features obscured by the heterogeneous nature of components in other complex systems .
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