Investigating existence of chaos in short and long term dynamics of Moroccan exchange rates

This paper proposes a new methodology to investigate presence of chaos in exchange rate time series by combining wavelet transform and Lyapunov exponent estimation. In particular, stationary wavelet transform (SWT) is applied to exchange rate original time series for decomposition purpose. As a result, approximation and details coefficients are extracted. They are used to represent long and short term dynamics of the original exchange rate time series. Then, largest Lyapunov exponent is estimated for each type of dynamics to check for presence of chaos. Our methodology is applied to several Moroccan exchange rate time series. The empirical results show that, in general, the hypothesis of chaotic structure is accepted for currency levels but it is rejected for currency returns on both long and short dynamics. In addition, long and short dynamics exhibit different chaotic patterns in some exchange rate time series. Our approach may be useful to understand chaotic behaviour in original exchange rate time series.