We introduce block bootstrap techniques that are (first order) valid in recursive estimation frameworks. There-after, we present two examples where predictive accuracy tests are made operational using our new bootstrap proce-dures. 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 amongst 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 (1999); 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.

Abstract not found

Abstract. When comparing two competing approximate models, the one having smallest ‘expected true error ’ is closest to the data generating process (according to the specified loss function) and is therefore to be preferred. In this paper we consider a data-driven method of testing whether two competing approximate models, for instance a parametric and a nonparametric model, are equivalent in terms of their expected true error (i.e., their expected performance on unseen data drawn from the same data generating process). The proposed test is quite flexible with regards to the types of models and data types that can be compared (i.e., time-series, cross section, panel etc.). Moreover, by applying our method to time-series models we can overcome two of the drawbacks associated with existing approaches, namely, the reliance on only one split of the data and the need to have a sufficiently large hold-out sample in order for the test to have power. Some useful graphical summaries are also presented. Finite-sample performance and several illustrative applications are considered. 1.