The multiscale causal dynamics of foreign exchange markets

This paper relies on wavelet multiresolution analysis to investigate the dependence structure and predictability of currency markets across different timescales. It explores the nature and direction of causality among the exchange rates with respect to the US dollar of the most widely traded currencies, namely Euro, Great Britain Pound and Japanese Yen. The timescale analysis involves the estimation of linear, nonlinear and spectral causal relationships of wavelet components and aggregate series as well as the investigation of their out-of-sample predictability. Moreover, this study attempts to probe into the micro-foundations of across-scale causal heterogeneity on the basis of trader behavior with different time horizons. The examined period starts from the introduction of the Euro and covers the dot-com bubble, the financial crisis of 2007–2010 and the Eurozone debt crisis. Technically, this paper presents an invariant discrete wavelet transform that deals efficiently with phase shifts, dyadic-length and boundary effects. It also proposes a new entropy-based methodology for the determination of the optimal decomposition level and a wavelet-based forecasting approach. Overall, there is no indication of a global causal behavior that dominates at all timescales. In the out-of-sample analysis wavelets clearly outperform the random walk for the volatility series. Moreover, the synergistic application of wavelet decomposition and artificial neural networks provided with an enhanced predictability in many forecast horizons for the returns. These results may have important implications for market efficiency and predictability.