June 25, 2003 12:17 WSPC/104-IJTAF 00195 International Journal of Theoretical and Applied Finance Vol. 0, No. 0 (2003) 1–11 c  World Scientiﬁc Publishing Company MEASURING THE COMPLEXITY OF CURRENCY MARKETS BY FRACTAL DIMENSION ANALYSIS ABDOL S. SOOFI University Plaza, University of Wisconsin-Platteville, Platteville, WI 53818-3099, USA sooﬁ@uwplatt.edu ANDREAS GALKA Institute of Experimental and Applied Physics, University of Kiel, Germany galka@physik.uni-kiel.de Received 8 November 2002 Accepted 17 December 2002 We use the theory of nonlinear dynamical systems to measure the complexity of currency markets by estimating the correlation dimension of the returns of the Dollar/Pound and Dollar/Yen daily exchange rates (the spot rates). We test the signiﬁcance of the re- sults by comparing them to correlation dimension estimates for surrogate time series, i.e. stochastic linear time series with the same power spectrum and amplitude distribu- tion as given by the original data. We ﬁnd discernible nonlinear structure in the returns of the Dollar/Pound daily rate. Keywords : Complexity; correlation dimension; exchange rate, surrogate data. 1. Introduction In recent years in analyses of complex systems new ideas and approaches that have originated in statistical physics, probability theory and ergodic theory are used. These ideas and approaches which are summarized now as the theory of nonlinear dynamical systems contain a number of new techniques that are highly valued for the analysis of complex systems arising in economics and ﬁnance. Increasingly, researchers in economics are relying on the theory of nonlinear dynamics as a powerful framework for providing answers to various problems in economics for which traditional approaches were ineﬀective in giving solutions (see Sooﬁ and Cao [21]). As a crucial component of this theory, state space reconstruc- tion by time-delay embedding, that was proposed by Takens [23] (whose results were later extended by Sauer et al. [18]), has become widely employed. In contrast to more traditional linear stochastic modelling, this theory stresses the deterministic aspect of given dynamical systems and tries to avoid stochastic elements as much as possible. The dynamics of a nonlinear deterministic system is said to display chaos, 1