Taking advantage of biased proxies for forecast evaluation

This paper rehabilitates biased proxies for the assessment of the predictive accuracy of competing forecasts. By relaxing the ubiquitous assumption of proxy unbiasedness adopted in the theoretical and empirical literature, we show how to optimally combine (possibly) biased proxies to maximize the probability of inferring the ranking that would be obtained using the true latent variable, a property that we dub proxy reliability. Our procedure still preserves the robustness of the loss function, in the sense of Patton (2011b), and allows testing for equal predictive accuracy, as in Diebold and Mariano (1995). We demonstrate the usefulness of the method with compelling empirical applications on GDP growth, financial market volatility forecasting, and sea surface temperature of the Nino 3.4 region.