Abstract

Forecasters and applied econometricians are often interested in comparing the predictive accuracy of nested competing models. A leading example of a context in which competing models are nested is when predictive ability is equated with “out-of-sample Granger causality”. In particular, it is often of interest to assess whether historical data from one variable are useful when constructing a forecasting model for another variable, and hence our use of terminology such as “out-of-sample Granger causality ” (see e.g. Ashley, Granger and Schmalensee (1980)). In this paper we examine and discuss three key issues one is faced with when constructing predictive accuracy tests, namely: the contribution of parameter estimation error, the choice of linear versus nonlinear models, and the issue of (dynamic) misspecification, with primary focus on the latter of these issues. One of our main conclusions is that there are a number of easy to apply statistics constructed using out of sample conditional moment conditions which are robust to the presence of dynamic misspecification under both hypothesis. We provide some new Monte Carlo findings and empirical evidence based on the use of such tests. In particular, we analyze the finite sample properties of the consistent out of sample test of Corradi and Swanson (2002) using data generating processes calibrated with

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