Inference on Predictability of Foreign Exchange Rates via Generalized Spectrum and Nonlinear Time Series Models

It is often documented, based on autocorrelation, variance ratio and power spectrum, that exchange rates approximately follow a martingale process. Because autocorrelation, variance ratio and spectrum check serial uncorrelatedness rather than martingale difference, they may deliver misleading conclusions in favor of the martingale hypothesis when the test statistics are insigniÞcant. In this paper, we explore whether there exists a gap between serial uncorrelatedness and martingale difference for exchange rate changes, and if so, whether nonlinear time series models admissible in the gap can outperform the martingale model in out-of-sample forecasts. Applying the generalized spectral tests of Hong (1999) to Þve major currencies, we Þnd that the changes of exchange rates are often serially uncorrelated, but there exists strong nonlinearity in conditional mean, in addition to the well-known volatility clustering. To forecast the conditional mean, we consider the linear autoregressive, autoregressive polynomial, artiÞcial neural network and functional-coefficient models, as well as their combination. The functional coefficient model allows the autoregressive coefficients to depend on investment positions via an moving average technical trading rule. We evaluate out-of-sample forecasts of these models relative to the martingale model, using four criteria– the mean squared forecast error, the mean absolute forecast error, the mean forecast trading return, and the mean correct forecast direction. White’s (2000) reality check method is used to avoid data-snooping bias. It is found that suitable nonlinear models, particularly their combination, do have superior predictive ability over the martingale model for some currencies in terms of certain forecast evaluation criteria.