Forecast Rationality Tests Based on Multi-Horizon Bounds
Andrew J. Patton Duke University Allan Timmermann University of California, San Diego December 1, 2010
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 longhorizon 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' Greenbook forecasts is presented. s
Keywords: Forecast optimality, real-time data, survey forecasts, forecast horizon. J.E.L. Codes: C53, C22, C52
We thank Tim Bollerslev, Frank Diebold, Mark Watson, and Ken West for comments and discussions. We also thank seminar participants at the Triangle Econometrics Workshop, Federal Reserve Bank at St. Louis, University of Michigan, Rice University, UCSD, EC 2 conference on real-time econometrics (December, 2009), IIF conference in San Diego (June, 2009), and the sixth forecasting symposium at the ECB. We are grateful to Jonathan Wright for providing the data used in the empirical analysis.
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Introduction

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