We examine the asymptotic and finite-sample properties of tests for equal forecast accuracy and encompassing applied to 1-step ahead forecasts from nested parametric models. We first derive the asymptotic distributions of two standard tests and one new test of encompassing. Tables of...

This paper uses Monte Carlo experiments to examine the small-sample properties of some commonly used tests of equal forecast accuracy. The study pays particular attention to test power, evaluated using both asymptotic and empirical critical values. In addition to evaluating different tests, this...

One of the approaches to compare forecasts is to test whether the loss from a benchmark prediction is smaller than the others. The test can be embedded into the general problem of testing functional inequalities using a one-sided Kolmogorov-Smirnov functional. This paper shows that such a test...

This paper examines the asymptotic and finite-sample properties of tests of equal forecast accuracy applied to direct, multi-step predictions from both non-nested and nested linear regression models. In contrast to earlier work in the literature, our asymptotics take account of the real-time,...

This paper introduces the model confidence set (MCS) and applies it to the selection of models. An MCS is a set of models that is constructed so that it will contain the best model with a given level of confidence. The MCS is in this sense analogous to a confidence interval for a parameter. The...

We propose a new test for superior predictive ability. The new test compares favorable to the reality check for data snooping (RC), because the former is more powerful and less sensitive to poor and irrelevant alternatives. The improvements are achieved by two modifications of the RC. We employ...

This paper examines the asymptotic and finite-sample properties of tests of equal forecast accuracy and encompassing applied to predictions from nested long-horizon regression models. We first derive the asymptotic distributions of a set of tests of equal forecast accuracy and encompassing,...

We investigate a test of conditional predictive ability described in Giacomini and White (2006; Econometrica). Our main goal is simply to demonstrate existence of the null hypothesis and, in doing so, clarify just how unlikely it is for this hypothesis to hold. We do so using a simple example of...

This paper presents analytical, Monte Carlo, and empirical evidence on the effects of structural breaks on tests for equal forecast accuracy and forecast encompassing. The forecasts are generated from two parametric, linear models that are nested under the null. The alternative hypotheses allow...

Multivariate distributional forecasts have become widespread in recent years. To assess the quality of such forecasts, suitable evaluation methods are needed. In the univariate case, calibration tests based on the probability integral transform (PIT) are routinely used. However, multivariate...