A Unified Predictability Test Using Weighted Inference and Random Weighted Bootstrap

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.