We propose two robust methods for testing hypotheses on unknown parameters of predictive regression models under heterogeneous and persistent volatility as well as endogenous, persistent and/or fat-tailed regressors and errors. The proposed robust testing approaches are applicable both in the case of discrete and continuous time models. Both of the methods use the Cauchy estimator to effectively handle the problems of endogeneity, persistence and/or fat-tailedness in regressors and errors. The difference between our two methods is how the heterogeneous volatility is controlled. The first method relies on robust t-statistic inference using group estimators of a regression parameter of interest proposed in Ibragimov and Muller, 2010. It is simple to implement, but requires the exogenous volatility assumption. To relax the exogenous volatility assumption, we propose another method which relies on the nonparametric correction of volatility. The proposed methods perform well compared with widely used alternative inference procedures in terms of their finite sample properties.

翻译：我们提出了两种稳健方法，用于在异质且持续的波动性以及内生、持续和/或重尾的回归变量与误差下，检验预测回归模型中未知参数的假设。所提出的稳健检验方法适用于离散时间模型和连续时间模型。这两种方法均使用柯西估计量来有效处理回归变量和误差中的内生性、持续性和/或重尾性问题。两种方法的区别在于对异质波动性的控制方式不同。第一种方法依赖于Ibragimov和Muller（2010）提出的回归参数组估计量的稳健t统计量推断。该方法易于实施，但需假设外生波动性。为放宽外生波动性假设，我们提出了另一种基于非参数波动性校正的方法。与广泛使用的替代推断程序相比，所提方法在有限样本性质方面表现优异。