A Unified Predictability Test Using Weighted Inference and Random Weighted Bootstrap
针对预测回归中条件异方差和预测变量非零截距的挑战，提出一种基于加权推断和随机加权自举的统一可预测性检验方法，模拟显示其在不同场景下尺寸准确，实证发现对S&P 500月收益有更强预测证据。
Abstract Predictive regressions play a pivotal role in assessing the predictability of returns for financial assets. However, the existence of a non-zero intercept in the predictive variable poses challenges for the popular IVX method, as the statistical properties of a nearly integrated predictive variable differ significantly with and without an intercept. This article presents a novel unified predictability test utilizing weighted inference and random weighted bootstrap. It addresses challenges posed by both conditional heteroscedasticity in linear predictive regression and the presence of a non-zero intercept in the predictor variable. Simulation results demonstrate the accurate size of the proposed test across various scenarios, including stationary, near unit root, unit root, mildly integrated, mildly explosive, and zero and non-zero intercepts. In an empirical application, we employ the proposed test to investigate the predictive capacity of eleven economic and financial variables on the monthly returns of the S&P 500 from 1980 to 2019. The findings reveal stronger evidence of predictability compared to the instrumental variable-based test.