Testing predictability of stock returns under possible bubbles

This study reexamines stock return predictability via several financial variables and an investor sentiment index. We develop an IVX bubble-based Wald statistic (IVX-BUB) which extends the IVX-based test (IVX-KMS) proposed by Kostakis, Magdalinos and Stamatogiannis (2015) and accounts for the potential bubble effect in the predictive regression. Simulation results indicate that IVX-BUB performs reasonably well when bubbles exist, while IVX-KMS displays severe size distortion in highly persistent predictors. In the empirical study, we consider the monthly excess returns of S&P 500 during 1927–2016 and identify six bubble episodes using the real-time date-stamping strategy proposed by Phillips, Shi and Yu (2015a, 2015b). The empirical results show that IVX-BUB produces fewer significant individual predictors and their combinations than IVX-KMS, but both methods provide evidence in favor of the strong predictive ability of the investor sentiment index.