Moment-Based Tests under Parameter Uncertainty

• 成果类型: Review
• 署名作者: Bontemps, Christian
• 署名单位: Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Ecole Nationale de l'Aviation Civile (ENAC); Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics
• 刊物名称: REVIEW OF ECONOMICS AND STATISTICS
• ISSN/ISSBN: 0034-6535
• DOI: 10.1162/rest_a_00745
• 发表日期: 2019-03
• 页码: 146-159
• 关键词: value-at-risk; generalized-method; normality; specification; inference; skewness; kurtosis; robust; fit

摘要

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.