Bootstrap procedures for recursive estimation schemes with application to forecast model selection

In recent years it has become apparent that many of the classical testing procedures used to select amongst alternative economic theories and economic models are not realistic. In particular, researchers have become more aware of the fact that parameter estimation error and data dependence play a crucial role in test statistic limiting distributions, a role which had hitherto been ignored to a large extent. Given the fact that one of the primary ways for comparing different models and theories is via use of predictive accuracy tests, it is perhaps not surprising that a large literature on the topic has developed over the last 10 years, including, for example, important papers by Diebold and Mariano (1995), West (1996), and White (2000). In this literature, it is quite common to compare multiple models (which are possibly all misspecified - i.e. they are all approximations of some unknown true model) in terms of their out of sample predictive ability, for given loss function. Our objectives in this paper are twofold. First, we introduce block bootstrap techniques that are (first order) valid in recursive estimation frameworks. Thereafter, we present two applications where predictive accuracy tests are made operational using our new bootstrap procedures. One of the applications outlines a consistent test for out-of-sample nonlinear Granger causality, and the other outlines a test for selecting amongst multiple alternative forecasting models, all of which may be viewed as approximations of some unknown underlying model...