Fractal structure in the Chinese yuan/US dollar rate

Price changes of the Chinese yuan/US dollar rate are found to display a Sierpinski triangle in an Iterative Function System clumpiness test. This fractal structure commonly emerges in “the chaos gameâ€, where randomness coexists with deterministic rules. We show that a threshold model with four states, two deterministic and two stochastic is able to replicate the properties of the yuan/dollar returns in general, and the Sierpinski triangle in particular.

Hurst exponents, power laws, and efficiency in the Brazilian foreign exchange market

We find evidence of weak informational efficiency in the Brazilian daily foreign exchange market using Hurst exponents (Hurst 1951, 1955, Feder 1988), which offer an alternative (from statistical physics) to traditional econometric gauges. We show that a trend toward efficiency has been reverted since the crisis of 1999. We also find power laws (Mantegna and Stanley 2000) in means, volatilities, the Hurst exponents, autocorrelation times, and complexity indices of returns for varying time lags.econophysics

The Chinese Chaos Game

The yuan-dollar returns prior to the 2005 revaluation show a Sierpinski triangle in an iterated function system clumpiness test. Yet the fractal vanishes after the revaluation. The Sierpinski commonly emerges in the chaos game, where randomness coexists with deterministic rules [2, 3]. Here it is explained by the yuan’s pegs to the US dollar, which made more than half of the data points close to zero. Extra data from the Brazilian and Argentine experiences do confirm that the fractal emerges whenever exchange rate pegs are kept for too long.

Synge's dynamic problem for two isolated point charges. A new method to find global solutions for Functional Differential Equations System

Synge's problem consists in to determine the dynamics of two point electrical charges interacting through their electromagnetic fields, without to take into account the radiation terms due to the self-forces in each charge. We discuss how this problem is related to the question on to establish initial conditions for the electromagnetic fields that are compatible with the two point charges system isolation, that is, the charges are free from the action of external forces. This problem stems from the existence of inter-temporal constraints for the charges trajectories, which implies that the relativistic Newton equations for the charges is not a system of ODEs, but rather a system of Functional Differential Equations (FDEs). We developed a new method to obtain global solutions that satisfies this system of FDEs and a given initial condition for the charges positions and velocities. This method allows the construction of a recursive numerical algorithm that only use integration methods for ODEs systems. Finally, we apply this algorithm to obtain numerical approximations for the quasi-circular solutions that are predicted in Synge's problem.Comment: 32 pages, 10 Figures, 2 Tables, Preprint Article. J. Phys. A: Math. Theor (2023

Characteristic function approach to the sum of stochastic variables

This paper puts forward a technique based on the characteristic function to tackle the problem of the sum of stochastic variables. We consider independent processes whose reduced variables are identically distributed, including those that violate the conditions for the central limit theorem to hold. We also consider processes that are correlated and analyze the role of nonlinear autocorrelations in their convergence to a Gaussian. We demonstrate that nonidentity in independent processes is related to autocorrelations in nonindependent processes. We exemplify our approach with data from foreign exchange rates.econophysics; central limit theorem; characteristic function; reduced variables; autocorrelation