Robust Cauchy-Based Methods for Predictive Regressions

2025-11-12

AI Summary

This paper addresses size distortion in standard inference for financial regression models arising from endogeneity, near-nonstationarity, heavy-tailed error distributions, and persistent volatility. We propose a robust inference framework based on Cauchy estimation. Two novel methodologies are introduced: grouped t-statistic inference and Cauchy-OLS hybrid estimation—both applicable uniformly to continuous- and discrete-time models. The framework substantially improves finite-sample stability and test power under nonstationary, heavy-tailed, and heteroskedastic volatility environments. Monte Carlo simulations demonstrate its superiority over conventional approaches, including OLS, IV, and QMLE-based methods. Empirically, we find robust predictive power of the dividend–price ratio for excess stock returns, whereas the earnings–price ratio is insignificant. Our framework provides a new, reliable tool for causal inference in complex financial time series characterized by nonstandard dependence and distributional features.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Intelligent Robots: State Estimation

Application Category

• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Economics, Online Markets and Human Computation: Sustainability of Web economics

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.

Problem

• Develops robust inference methods for predictive regressions with persistent regressors
• Addresses size distortions from heavy-tailed data and persistent volatility
• Tests predictive power of financial ratios on stock returns

Innovation

• Cauchy-based robust inference for predictive regressions
• Hybrid Cauchy-OLS method addressing endogeneity and heavy tails
• t-statistic group inference mitigating size distortions