The analysis of monthly exchange rates is carried out using a model of McCallum, which is based on the concept of Rational Expectations. Applying the model to the CHF/USD exchange rate starting a misspecification analysis, the RE component appears to be a weak point of the model. The theory of rational beliefs of M. Kurz generalizes the RE concept introducing special consideration of Data Generating Processes (DGP). We find, however, some evidence speaking against the rational belief approach (with respect to the CHF/USD exchange rate) which is related to regime switchings and the presence of unobserved variables in the data-generating process. It appears that the rationality of economic agents depends on complex cognitive processes not discussed by Kurz, but taken into account in a ''story'' by Paul De Grauwe. This story will be supplemented in Part II of the paper in order to eliminate the RE component and to proceed with the misspecification analysis of McCallum's model.