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 economies are 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.
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