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Combining p-values for Multivariate Predictive Ability Testing

Urga, G. ORCID: 0000-0002-6742-7370 & Spreng, L. (2022). Combining p-values for Multivariate Predictive Ability Testing. Journal of Business and Economic Statistics, 41(3), pp. 765-777. doi: 10.1080/07350015.2022.2067545


In this paper, we propose an intersection-union test for multivariate forecast accuracy based on the combination of a sequence of univariate tests. The testing framework evaluates a global null hypothesis of equal predictive ability using any number of univariate forecast accuracy tests under arbitrary dependence structures, without specifying the underlying multivariate distribution. An extensive MonteCarlo simulation exercise shows that our proposed test has very good size and power properties under several relevant scenarios, and performs well in both low- and high-dimensional settings. We illustrate the empirical validity of our testing procedure using a large dataset of 84 daily exchange rates running from 1 January 2011 to 1 April 2021. We show that our proposed test addresses inconclusive results that often arise in practice.

Publication Type: Article
Additional Information: © 2022 The Authors. Published with license by Taylor & Francis Group, LLC. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
Publisher Keywords: Forecasting Evaluation; Predictive Accuracy; Intersection-Union Tests; Exchange Rates
Subjects: H Social Sciences > HB Economic Theory
H Social Sciences > HF Commerce
Q Science > QA Mathematics
Departments: Bayes Business School > Finance
SWORD Depositor:
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