Robust Cauchy-Based Methods for Predictive Regressions

TL;DR

This paper introduces robust inference methods for predictive regressions using Cauchy-based techniques to handle endogeneity, heavy tails, and persistent volatility, with demonstrated effectiveness through simulations and stock return analysis.

Contribution

It proposes two novel Cauchy-based tests for predictive regressions that improve inference robustness under challenging data conditions.

Findings

The proposed tests reduce size distortions in finite samples.

Simulation results show favorable performance across various scenarios.

Empirical analysis finds dividend-price ratio predicts stock returns, earnings-price ratio does not.

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.