This paper investigates models for the euro exchange rate against the currencies of Denmark, Poland, theUnited States, and the United Kingdom. The objective of this paper is to compare different methods of modeling andout-of-sample forecasting. One of the techniques is cointegration relation, which is implemented through a vector errorcorrection model. The existence of cointegration supports the long-run relationship between the nominal exchange rateand a number of fundamental variables. The evidence presented in this paper shows that a simple multivariate randomwalk model tends to have superior predictive performance, compared to other exchange rate models, for a period of lessthan one year.