In this paper, we study the estimation of the threshold predictive regression model with hybrid stochastic local unit root predictors. We demonstrate the estimation procedure and derive the asymptotic distribution of the least square estimator and the IV based estimator proposed by Magdalinos and Phillips (2009), under the null hypothesis of a diminishing threshold effect. Simulation experiments focus on the finite sample performance of our proposed estimators and the corresponding predictability tests as in Gonzalo and Pitarakis (2012), under the presence of threshold effects with stochastic local unit roots. An empirical application to stock return equity indices, illustrate the usefulness of our framework in uncovering regimes of predictability during certain periods. In particular, we focus on an aspect not previously examined in the predictability literature, that is, the effect of economic policy uncertainty.