Distinguishing between stochastic and deterministic behavior in high frequency foreign exchange rate returns: Can non-linear dynamics help forecasting?

Abstract

This paper investigates the dynamic properties of high frequency foreign exchange rate returns. Using hourly data for four exchanges rates, the British Pound, the Deutschemark, the Japanese Yen and Swiss Franc, we attempt to differentiate between stochastic and deterministic behavior in hourly rates of returns. While the autocorrelation coefficients and the Brock-Dechert-Scheinkman test point to the presence of some non-linear dependence, correlation dimension estimates reveal little evidence in favor of low-dimensional chaos. The analysis appears to support the view that although it is not possible to exploit deterministic non-linear dependence in exchange rate time series in order to improve short-term forecasting, non-linear stochastic models can be used for conditional volatility forecasts.