Long-run dynamics of exchange rates: A multi-frequency investigation

The empirical observation that purchasing power parity (PPP) holds in the long run but not in the short run has enjoyed a near-consensus status in international finance literature. However, a similar degree of agreement has not been reached with respect to the exact horizon of this "long run" aspect. To shed light on this matter, a novel approach is adopted in this paper to combine conventional time series methodology with insights from multi-frequency analyses. In particular, we simultaneously explore price-exchange-rate dynamics not only through time, but also at various horizons via a wavelet decomposition. Unit root tests applied to wavelet-based decomposed real exchange rates indicates that PPP holds at horizons consistent with the literature. With respect to the predictive value of our approach, we show that our decomposed measures provide guidance to future movements of real change rates. Additionally, we find that nominal exchange-rate dynamics are dominated by activities corresponding to low frequencies. Results from this study thus enable researchers and practitioners to establish an exchange-rate modelling framework with increased efficiency.