Predictive extremile regression with persistent covariates: IVX-ER approach
提出极值回归作为预测回归框架中分位数回归的替代，结合IVX滤波处理持久协变量问题，推导估计量的理论性质，并通过蒙特卡洛模拟和股票收益实证验证其稳健性和效率。
This paper introduces extremile regression (ER) as an alternative to quantile regression (QR) in the predictive regression framework under various persistence regimes. We establish the theoretical properties of ER estimators, which, in contrast to their QR counterparts, admit closed-form expressions and facilitate a more tractable asymptotic analysis. To address distortions in ordinary ER estimation under local-to-unity and unit-root settings, we integrate IVX filtering into predictive ER modeling. The resulting IVX-ER estimators converge to (mixture) normal distributions across all persistence levels. We further develop an IVX-ER test statistic for predictability and derive its null limiting distribution. Monte Carlo simulations confirm the finite-sample accuracy of the ER estimators and demonstrate the robustness and efficiency of the IVX-ER framework under diverse persistence patterns and heavy-tailed innovations. In an empirical application to long-horizon stock returns, the results reveal a fundamental shift in market dynamics, where the broad-based predictive power of valuation, corporate-finance, and bond-yield measures in the historical period gives way to a more specialized, interaction-driven regime in the modern era, with certain variable combinations emerging as robust predictors across the entire return distribution while others become specialized indicators for downside risk.