Comment on 'forecast Rationality Tests Based on Multi-horizon Bounds'

I enjoyed reading yet another paper by Patton and Timmermann (PT hereinafter) and feel that it has broken new ground in testing the rationality of a sequence of multi-horizon fixed target forecasts. Rationality tests are not new in the forecasting literature, but the idea of testing the monotonicity properties of second moment bounds across several horizons is novel and can suggest possible sources of forecasting failure. The basic premise is that since forecasts at shorter horizons are based on more information, they should on the average be more accurate than their longer horizon counterparts. The internal consistency properties of squared errors, squared forecasts, squared forecast revisions and the covariance between the target variable and the forecast revision are tested as inequality constraints across horizons. They also generalize the single horizon Mincer-Zarnowitz (MZ) unbiasedness test by estimating a univariate regression of the target variable on the longest-horizon forecast and all intermediate forecast revisions. Using a Monte Carlo experiment and Greenbook forecasts of four macro variables, PT show that the covariance bound test and the generalized MZ regression using all interim forecast revisions have good power to detect deviations from forecast optimality. I am sure we will be using, extending and finding caveats with some of the testing proposals suggested in this paper for years to come. 2. THEORETICAL CONSIDERATIONS