Working Paper: CEPR ID: DP8194
Authors: Andrew J. Patton; Allan G. Timmermann
Abstract: 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.
Keywords: Forecast Horizon; Forecast Optimality; Realtime Data; Survey Forecasts
JEL Codes: C22; C52; C53
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Monte Carlo simulations (C15) | demonstrate better power of proposed tests compared to conventional methods (C52) |
| mean squared forecast error (MSFE) (C53) | weakly increasing function of forecast horizon (C53) |
| variance of forecasts (C53) | weakly decreasing function of forecast horizon (C53) |
| optimal updating of forecasts (C53) | variance of forecast revisions exceeds twice covariance between forecast revisions and actual values (C53) |
| covariance of forecast errors with target variable (C53) | decrease as forecast horizon increases (G17) |
| new optimal revision test (C61) | identifies deviations from forecast optimality (C53) |