Testing predictability of stock returns under quantile regression: A bootstrapping double-weighted approach

In financial econometrics, it is empirically challenging to test the predictability of lagged predictors with varying levels of persistence in predictive quantile regression. A recent double-weighted method developed by Cai, Chen, and Liao (2023) has demonstrated desirable local power properties for both non stationary and stationary predictors. In this article, we propose a strategy to improve the construction of the auxiliary variables in the double-weighted method. This improvement makes it applicable to a broader range of persistent types in empirical analysis. Furthermore, we propose a random weighted bootstrap procedure to address the challenges involved in conditional density estimation. Simulation results demonstrate the effectiveness of the proposed test in correcting size distortion at the lower and upper quantiles. Finally, we apply the proposed test to reassess the predictability of macroeconomic and financial predictors on stock returns across different quantile levels, finding fewer significant predictors at the tails compared to Cai, Chen, and Liao (2023). Our results highlight that this test serves as a more conservative inference tool for practitioners evaluating the predictability of financial returns.