Interpretation and use of sensitivity in econometrics, illustrated with forecast combinations

Abstract

Sensitivity analysis is important both for its own sake and in combination with diagnostic testing. We consider the question of how to use sensitivity statistics in practice, and in particular, how to judge whether the sensitivity is large or small. For this purpose, we distinguish between absolute and relative sensitivity, and highlight the context-dependent nature of sensitivity analysis. The relative sensitivity is then applied to forecast combinations, and sensitivity-based weights are introduced. All of the concepts are illustrated using the European yield curve. In this context, it is natural to consider the sensitivity to autocorrelation and normality assumptions. Different forecasting models are combined using equal, fit-based and sensitivity-based weights, and compared with the multivariate and random walk benchmarks. We show that the fit-based and sensitivity-based weights are complementary, but that the sensitivity-based weights perform better than other weights for long-term maturities.