New robust inference for predictive regressions

TL;DR

This paper introduces two robust inference methods for predictive regressions that effectively handle heterogeneity, persistence, and fat-tailed distributions in regressors and errors, applicable in both discrete and continuous time models.

Contribution

It presents novel robust testing approaches using the Cauchy estimator, including a simple method with exogenous volatility assumptions and a more flexible nonparametric volatility correction method.

Findings

Both methods outperform traditional inference procedures in finite samples.

The first method is easy to implement but requires exogenous volatility.

The second method relaxes volatility assumptions through nonparametric correction.

Abstract

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.