Testing Predictive Ability and Power Robustication

One of the approaches to compare forecasting methods is to test whether the risk from a benchmark prediction is smaller than the others. The test can be embedded into a general problem of testing inequality constraints using a one-sided sup functional. Hansen (2005) showed that such tests su¤er from asymptotic bias. This paper generalizes this observation, and proposes a hybrid method to robustify the power properties by coupling a one-sided sup test with a complementary test. The method can also be applied to testing stochastic dominance or moment inequalities. Simulation studies demonstrate that the new test performs well relative to the existing methods. For illustration, the new test was applied to analyze the forecastability of stock returns using technical indicators employed in White (2000). Key words and Phrases: Inequality Restrictions, Testing Predictive Ability, One-sided Sup Tests, Power Robusti…cation, Reality Check, Data Snooping JEL Classi…cations: C12, C14, C52, C53.