Some linear and nonlinear thoughts on exchange rates

Abstract

After discussing the inconclusive results of linear structural models as applied to exchange rates, this paper assesses the possibilities of using a particular form of nonlinear estimation, called Alternating Conditional Expectations, as: (i) a diagnostic tool, and (ii) a forecasting method. It contrasts the forecast performance of various linear (in levels, in differences, error correction) and nonlinear (in levels, in differences) specifications of a sticky-price monetary model, augmented by a relative wealth variable. The diagnostic results are as follows: the optimal transformations are almost always nonlinear, and often nonmonotonic. Forecasting results: in-sample and out-of-sample nonlinear forecasts yield substantial improvements over a random walk. However, in exercises with forecasts from rolling regressions, the random walk specification still dominates (over one-quarter forecast horizons), albeit only marginally and insignificantly so. Nonlinear specifications do slightly better than linear competitors at four-quarter horizons.