Multi-horizon uniform superior predictive ability revisited: A size-exploiting and consistent test

Verena Monschang, Mark Trede and Bernd Wilfling

No 10623, CQE Working Papers from Center for Quantitative Economics (CQE), University of Muenster

Abstract: Quaedvlieg (2021, Journal of Business & Economic Statistics) proposes a uniform Superior Predictive Ability (uSPA) test for comparing forecasts across multiple horizons. The procedure is based on a 'minimum Diebold-Mariano' test statistic, and asymptotic critical values are obtained via bootstrapping. We show, theoretically and via simulations, that Quaedvlieg's test is subject to massive size distortions. In this article, we establish several convergence results for the 'minimum Diebold- Mariano' statistic, revealing that appropriate asymptotic critical values are given by the quantiles of the standard normal distribution. The uSPA test modified this way (i) always keeps the nominal size, (ii) is size-exploiting along the boundary that separates the parameter subsets of the null and the alternative uSPA hypotheses, and (iii) is consistent. Based on the closed skew normal distribution, we present a procedure for approximating the power function and demonstrate the favorable finite-sample properties of our test. In an empirical replication, we find that Quaedvlieg's (2021) results on uSPA comparisons between direct and iterative forecasting methods are statistically inconclusive.

Keywords: Forecast evaluation; Joint-hypothesis testing; Stochastic dominance; Closed skew normal distribution (search for similar items in EconPapers)
JEL-codes: C12 C15 C52 C53 (search for similar items in EconPapers)
Pages: 25 pages
Date: 2023-11
New Economics Papers: this item is included in nep-ecm and nep-ets
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