Conditional Superior Predictive Ability[Modeling and Forecasting Realized Volatility]

This article proposes a test for the conditional superior predictive ability (CSPA) of a family of forecasting 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 conditional moment inequalities for time series data with general serial dependence, and we justify its asymptotic validity using a uniform non-parametric 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.