The dynamics of exchange rate time series and the chaos game

This work presents a novel method of reconstructing some relevant characteristics of exchange rate time series by the superposition of two components: a mostly deterministic one, the chaos game as expressed by the Yuan/USD exchange rate and a purely stochastic one, Gaussian white noise. We analyzed 20 economic systems with the average Index of Economic Freedom above 50. The considered characteristics (the Lempel-Ziv complexity index, the slimness of the distribution and the Iterated Function Systems clumpiness test) are well reproduced by the reconstruction process. Additional confirmation is obtained by an analysis of the exchange rate of the Romanian national currency as an example of an application of the method to a transition economy, and by an analysis of the time series of the Euro-zone as an example of an application to a multinational system using a shorter time series.