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The goal of developing a firmer theoretical understanding of inhomogenous temporal processes -- in particular, the waiting times in some collective dynamical system -- is attracting significant interest among physicists. Quantifying the deviations in the waiting-time distribution away from one generated by a random process, may help unravel the feedback mechanisms that drive the underlying dynamics. We analyze the waiting-time distributions of high frequency foreign exchange data for the best executable bid-ask prices across all major currencies. We find that the lognormal distribution yields a good overall fit for the waiting-time distribution between currency rate changes if both short and long waiting times are included. If we restrict our study to long waiting-times, each currency pairs distribution is consistent with a power law tail with exponent near to 3.5. However for short waiting times, the overall distribution resembles one generated by an archetypal complex systems model in which boundedly rational agents compete for limited resources. Our findings suggest a gradual transition arises in trading behavior between a fast regime in which traders act in a boundedly rational way, and a slower one in which traders decisions are driven by generic feedback mechanisms across multiple timescales and hence produce similar power-law tails irrespective of currency type.
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Movement tracks of wild animals frequently fit models of anomalous rather than simple diffusion, mostly reported as ergodic superdiffusive motion combining area-restricted search within a local patch and larger-scale commuting between patches, as highlighted by the Levy walk paradigm. Since Levy walks are scale invariant, superdiffusive motion is also expected within patches, yet investigation of such local movements has been precluded by the lack of accurate high-resolution data at this scale. Here, using rich high-resolution movement datasets ($>! 7 times 10^7$ localizations) from 70 individuals and continuous-time random walk modeling, we found subdiffusive behavior and ergodicity breaking in the localized movement of three species of avian predators. Small-scale, within-patch movement was qualitatively different, not inferrable and separated from large-scale inter-patch movement via a clear phase transition. Local search is characterized by long power-law-distributed waiting times with diverging mean, giving rise to ergodicity breaking in the form of considerable variability uniquely observed at this scale. This implies that wild animal movement is scale specific rather than scale free, with no typical waiting time at the local scale. Placing these findings in the context of the static-ambush to mobile-cruise foraging continuum, we verify predictions based on the hunting behavior of the study species and the constraints imposed by their prey.
Throughout economic history, the global economy has experienced recurring crises. The persistent recurrence of such economic crises calls for an understanding of their generic features rather than treating them as singular events. The global economic system is a highly complex system and can best be viewed in terms of a network of interacting macroeconomic agents. In this regard, from the perspective of collective network dynamics, here we explore how the topology of global macroeconomic network affects the patterns of spreading of economic crises. Using a simple toy model of crisis spreading, we demonstrate that an individual countrys role in crisis spreading is not only dependent on its gross macroeconomic capacities, but also on its local and global connectivity profile in the context of the world economic network. We find that on one hand clustering of weak links at the regional scale can significantly aggravate the spread of crises, but on the other hand the current network structure at the global scale harbors a higher tolerance of extreme crises compared to more globalized random networks. These results suggest that there can be a potential hidden cost in the ongoing globalization movement towards establishing less-constrained, trans-regional economic links between countries, by increasing the vulnerability of global economic system to extreme crises.
In high frequency financial data not only returns but also waiting times between trades are random variables. In this work, we analyze the spectra of the waiting-time processes for tick-by-tick trades. The numerical problem, strictly related with the real inversion of Laplace transforms, is analyzed by using Tikhonovs regularization method. We also analyze these spectra by a rough method using a comb of Diracs delta functions.
We introduce a framework to infer lead-lag networks between the states of elements of complex systems, determined at different timescales. As such networks encode the causal structure of a system, infering lead-lag networks for many pairs of timescales provides a global picture of the mutual influence between timescales. We apply our method to two trader-resolved FX data sets and document strong and complex asymmetric influence of timescales on the structure of lead-lag networks. Expectedly, this asymmetry extends to trader activity: for institutional clients in our dataset, past activity on timescales longer than 3 hours is more correlated with future activity at shorter timescales than the opposite (Zumbach effect), while a reverse Zumbach effect is found for past timescales shorter than 3 hours; retail clients have a totally different, and much more intricate, structure of asymmetric timescale influence. The causality structures are clearly caused by markedly different behaviors of the two types of traders. Hence, market nanostructure, i.e., market dynamics at the individual trader level, provides an unprecedented insight into the causality structure of financial markets, which is much more complex than previously thought.
A symmetry-guided definition of time may enhance and simplify the analysis of historical series with recurrent patterns and seasonalities. By enforcing simple-scaling and stationarity of the distributions of returns, we identify a successful protocol of time definition in Finance. The essential structure of the stochastic process underlying the series can thus be analyzed within a most parsimonious symmetry scheme in which multiscaling is reduced in the quest of a time scale additive and independent of moment-order in the distribution of returns. At the same time, duration of periods in which markets remain inactive are properly quantified by the novel clock, and the corresponding (e.g., overnight) returns are consistently taken into account for financial applications.
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