Wavelet Analysis and the Forward Premium Anomaly

Abstract

Forward and corresponding spot rates on foreign exchange markets differ so that forward rates cannot be used as unbiased predictors for future spot rates. This phenomenon has entered the literature under the heading of the Forward Premium Anomaly. We argue that standard econometric analyses implicitly assume that the relationship is time scale independent. We use wavelet analysis to decompose the exchange rate changes, and the forward premia, using the maximal overlap discrete wavelet transform (MODWT). Then we estimate the relationship on a scale-by-scale basis, thereby allowing for market inefficiencies such as noise, technical, and feedback trading as well as fundamental and rational trading. The results show that the forward premia serve as unbiased predictors for exchange rate changes (unbiasedness hypothesis) for certain time scales only. Monthly and weekly data concerning Euro, US-dollar and British Pound for forward periods from 1 month to 5 years is analysed. We find that the unbiasedness hypothesis cannot be rejected if the data is reconstructed using medium-term and long term components. This is most prevalent in the forward transaction periods up to 1 year.