Integration, cointegration and the forecast consistency of structural exchange rate models

We propose an alternative set of criteria for evaluating forecast rationality: the forecast and the actual series (1) have the same order of integration, (2) are cointegrated and (3) have a cointegrating vector consistent with long-run unitary elasticity of expectations. We denote forecasts that meet these criteria as 'consistent'. Forecasts generated from monetary models generally pass (1). However, using the Johansen procedure, cointegration fails to hold the longer the horizon. Of the cointegrated pairs, (3) is not generally rejected. Using the Horvath-Watson procedure, imposing the unitary coefficient restriction, we find fewer instances of consistency, although a higher proportion of the cases of consistency are found at the longer horizons.