The long swings in the spot exchange rates and the complex unit roots hypothesis

Abstract

This paper addresses whether the spot exchange rates display long swings and whether these swings are persistent. The null from the naïve random walk theory is that they do not: if they would be unit roots with positive drifts they would converge to infinity. However, if they would be driftless unit roots they would assign negative values, which is unrealistic. We test this by examining whether the yearly changes of spot exchange rates display complex conjugate unit roots against the stationary hypothesis. We reject the hypothesis that the yearly changes in exchange rates are stationary in favor of cyclical, complex unit roots. The periodogram based cycle duration analysis reveals that the long swings in the exchange rates are persistent.