详情
Inference on Predictability of Foreign Exchange Rates via Generalized Spectrum and Nonline
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.
