Nonparametric bootstrap procedures for predictive inference based on recursive estimation schemes

We introduce block bootstrap techniques that are (first order) valid in recursive estimation frameworks. Thereafter, we present two examples where predictive accuracy tests are made operational using our new bootstrap procedures. In one application, we outline a consistent test for out-of-sample nonlinear Granger causality, and in the other we outline a test for selecting among multiple alternative forecasting models, all of which are possibly misspecified. In a Monte Carlo investigation, we compare the finite sample properties of our block bootstrap procedures with the parametric bootstrap due to Kilian (Journal of Applied Econometrics 14 (1999), 491-510), within the context of encompassing and predictive accuracy tests. In the empirical illustration, it is found that unemployment has nonlinear marginal predictive content for inflation.