Dimensions and Lyapunov exponents from exchange rate series

Detecting the presence of deterministic chaos in economic time series is an important problem that may be solved by measuring the largest Lyapunov exponent. In this paper we present estimates of the largest Lyapunov exponent in daily data for the Swedish Krona vs Deutsche Mark, ECU, U.S. Dollar and Yen exchange rates. In order to estimate the dimension of the systems producing these exchange rate series, we also present estimates of the correlation dimension. We found indications of deterministic chaos in all exchange rate series. However, the estimates for the largest Lyapunov exponents are not reliable, except in the Swedish Krona-ECU case, because of the limited number of data points. In the Swedish Krona-ECU case, we found indications of a low-order chaotic dynamical system.