Moment-Based Tests under Parameter Uncertainty

Christian Bontemps (1, 2)

1 TSE-R - Toulouse School of Economics
2 ENAC - Ecole Nationale de l'Aviation Civile

This paper considers moment-based tests applied to estimated quantities. We propose a general class of transforms of moments to handle the parameter uncertainty problem. The construction requires only a linear correction that can be implemented in sample and remains valid for some extended families of nonsmooth moments. We reemphasize the attractiveness of working with robust moments, which lead to testing procedures that do not depend on the estimator. Furthermore, no correction is needed when considering the implied test statistic in the out-of-sample case. We apply our methodology to various examples with an emphasis on the backtesting of value-at-risk forecasts.

Domaines: Statistiques [stat]; Economies et finances

Christian Bontemps. Moment-Based Tests under Parameter Uncertainty. Review of Economics and Statistics, 2019, 101 (1), pp. 146-159. ⟨10.1162/rest_a_00745⟩. ⟨hal-02004687⟩