Robust Cauchy-Based Methods for Predictive Regressions
Rustam Ibragimov, Jihyun Kim, Anton Skrobotov
TL;DR
This work tackles inference in predictive regressions under endogeneity, near-nonstationarity, heavy tails, and persistent volatility by building on the Cauchy estimator. It introduces two robust procedures: a group-based t-statistic and a hybrid Cauchy-OLS test, both simple to implement and applicable to continuous and discrete time. The methods achieve correct size under broad conditions and exhibit strong finite-sample power across simulations that feature stochastic volatility, structural breaks, and regime switching. An empirical application to stock-return predictability shows the dividend–price ratio forecasting power, while the earnings–price ratio does not, illustrating the practical relevance of robust inference in financial econometrics.
Abstract
This paper develops robust inference methods for predictive regressions that address key challenges posed by endogenously persistent or heavy-tailed regressors, as well as persistent volatility in errors. Building on the Cauchy estimation framework, we propose two novel tests: one based on $t$-statistic group inference and the other employing a hybrid approach that combines Cauchy and OLS estimation. These methods effectively mitigate size distortions that commonly arise in standard inference procedures under endogeneity, near nonstationarity, heavy tails, and persistent volatility. The proposed tests are simple to implement and applicable to both continuous- and discrete-time models. Extensive simulation experiments demonstrate favorable finite-sample performance across a range of realistic settings. An empirical application examines the predictability of excess stock returns using the dividend-price and earnings-price ratios as predictors. The results suggest that the dividend-price ratio possesses predictive power, whereas the earnings-price ratio does not significantly forecast returns.