Nonlinearities in Exchange-Rate Dynamics: Chaos?

Abstract

In this paper we conduct a formal testing of the possibility of chaotic dynamics in daily exchange rate variables, namely exchange rate returns, volatility and normalized exchange rates. Substantial nonlinear dependence is found in exchange rate returns, even when GARCH-type structure is accounted for. Application of the tools from dynamical systems theory, such as correlation dimension and largest Lyapunov exponent calculation, strongly rejects the possibility of chaotic dynamics in the data. We show the importance of the Theiler correction to the Grassberger and Procaccia algorithm, omission of which can lead to a wrong conclusion of chaotic dynamics in some variables. Moreover, we suggest the necessity of considering a dynamic noise element in theoretical chaotic asset pricing models.

Keywords: Exchange rate dynamics, chaos, correlation dimension, Lyapunov exponents, BDS test

JEL Classification: C22, C49, C51, C63, F31, G12