Yang, Jian, Su, Xiaojing, and Kolari, James
Journal of Banking & Finance; Vol. 32 Issue 5, p. 729-740

Traditional autocorrelation and variance ratio tests are based on serial uncorrelatedness rather than martingale difference. As such, they do not capture potential nonlinearity-in-mean, which could lead to misleading inferences in favor of the martingale hypothesis. This paper employs various parametric and nonparametric nonlinear models as well as several model comparison criteria to examine the potential martingale behavior of Euro exchange rates in the context of out-of-sample forecasts. The overall evidence indicates that, while martingale behavior cannot be rejected for Euro exchange rates with major currencies such as the Japanese yen, British pound, and US dollar, there is nonlinear predictability in terms of economic criteria with respect to several smaller currencies.