Forecast Rationality Tests Based on Multi-Horizon Bounds

Forecast rationality under squared error loss implies various bounds on second moments of the data across forecast horizons. For example, the mean squared forecast error should be increasing in the horizon, and the mean squared forecast should be decreasing in the horizon. We propose rationality tests based on these restrictions, including new ones that can be conducted without data on the target variable, and implement them via tests of inequality constraints in a regression framework. A new optimal revision test based on a regression of the target variable on the long-horizon forecast and the sequence of interim forecast revisions is also proposed. The size and power of the new tests are compared with those of extant tests through Monte Carlo simulations. An empirical application to the Federal Reserve's Greenbook forecasts is presented.