Constructing Prediction Regions for Exchange Rate Path Forecasts: The Potential of Calibration

We examine and compare the performance of two novel competing approaches - simultaneous prediction regions and bootstrap joint prediction regions - in constructing uncertainty bands for the consensus path forecasts of the EUR/USD exchange rate. The prediction regions are constructed using actual out-of-sample path-forecast errors computed based on historical EUR/USD exchange rate data. We also explore the potential to improve the simultaneous prediction regions by applying the calibration principle. We use the family-wise prediction error rate to measure the joint accuracy of individual per-period intervals, and the likelihood ratio tests for interval accuracy to assess the conditional coverages. We find that the bootstrap joint prediction regions outperform the simultaneous prediction regions on a small evaluation sample. While calibration can improve the performance of simultaneous prediction regions, additional robustness exercises reveal that bootstrap joint prediction regions are generally more reliable from the perspective of unconditional coverage. On the other hand, neither method properly accounts for the dependence in the EUR/USD exchange rate path forecasts.