The exchange rate is recognised as a particularly tricky subject for modelling and prediction. The problems of unobservables such as expectations, of simultaneity, and of policy changes (both overt and covert) in the sample period to which models must be fitted may account for the disappointing results of recent attempts to test theories of exchange rate determination. This paper develops an appropriate empirical model to deal with these problems; it allows consideration of the proper interpretation of theoretical assumptions and determination of how far modelling for ex ante prediction can succeed. The exchange rate is recognised as a particularly tricky subject for modelling and prediction. The problems of unobservables such as expectations, of simultaneity, and of policy changes (both overt and covert) in the sample period to which models must be fitted may account for the disappointing results of recent attempts to test theories of exchange rate determination-see for example the pessimistic conclusions of Hacche and Townend (1981). The aim of this paper is to develop an appropriate empirical model for these purposes, to consider in particular the proper interpretation of theoretical assumptions, and to determine how far, in this case, modelling for ex ante prediction can succeed. The core of the model is the view of the exchange rate as a price determined in an efficient market with low transactions costs and well-informed transactors. In this view the observed rate represents a market equilibrium apart from random deviations, and where equilibrium is contingent upon an expected future state of the world, the expectations are assumed rational in the sense of being unbiased relative to a given information set. The implications of strong and weak forms of rationality, in which the information set is either relatively wide or narrow, must however be carefully distinguished. Under the most extreme rationality hypothesis it will not be possible to improve on a simple modified random walk model for ex ante prediction, and so the role of additional lagged variables is an important empirical issue. (Compare for example the life-cycle model of consumption as in Hall (1978) and see also Davidson and Hendry (1981).) Although there has been a good deal of investigation of exchange market rationality-e.g. Frenkel (1981), Levich (1978), Hacche and Townend (1981), Baillie, Lippens and MacMahon (1983)-the evidence remains inconclusive. Another important issue which the paper seeks to understand, separate from although related to the rationality question, is the volatility of the exchange rate relative to the variables which might be expected to explain it. Explanation in terms of a linear short-run equilibrium model-e.g. the overshooting hypothesis-does not account convincingly for the very large shifts periodically observed in response to apparently minor stimuli. A theoretical justification for a nonlinear econometric framework is developed and this model is found to dominate the linear alternative on goodness-of-fit criteria.