Fractal Structure in the Chinese Yuan-US Dollar Rate

Raul Matsushita, University of Brasilia
Iram Gleria, Federal University of Alagoas
Annibal Figueiredo, University of Brasilia
Sergio Da Silva, Federal University of Rio Grande Do Sul

Abstract

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 game”, 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 changes in general, and the Sierpinski triangle in particular.