Conditional Superior Predictive Ability

This paper proposes a test for the conditional superior predictive ability (CSPA) of a family of forecast methods with respect to a benchmark. The test is functional in nature: Under the null hypothesis, the benchmark’s conditional expected loss is no more than those of the competitors, uniformly across all conditioning states. By inverting the CSPA tests for a set of benchmarks, we obtain confidence sets for the uniformly most superior method. The econometric inference pertains to testing a system of conditional moment inequalities for time series data with general serial dependence, and we justify its asymptotic validity using a uniform nonparametric inference method based on a new strong approximation theory for mixingales. The usefulness of the method is demonstrated in empirical applications on volatility and inflation forecasting.

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