Chaos in the Foreign Exchange Markets

Abstract

In the late 80’s, nonlinear dynamic systems known as deterministic chaos attracted new interest among economists (Boldrin and Woodford, 1990; Brock and Dechert, 1991; Grandmont, 1992; DeGrauwe and Dewachter, 1993). With only a few degrees of freedom - i.e. a low-dimensional¹ fractal attractor - such systems can indeed mimic a stochastic behaviour and thus reconcile the classical deterministic view with the apparent unpredictability and randomness observed in real-world data (Mirowski, 1990). These theoretical developments are promising as they provide a natural extension to traditional low-dimensional macro-economic models (see chapter 1) but have so far been limited to the analysis of the conditions of emergence of multiple and unstable equilibria. Ultimately, their empirical relevance rests on findings that detect chaotic behaviour in real-world data. Besides, the empirical investigation of chaos could reveal itself very useful for the construction of theoretical models. Indeed, empirical tests of chaos can yield some information on the structure of theoretical models such as the number of independent variables without depending on the specific functional form of the model. Moreover, they include the detection of simpler dynamics such as a unique steady state or multiple equilibria (see chapter 1). Empirical tests of chaos can thus be considered as very general tests of the adequacy of low-dimensional structural or macro-economic models.