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

Estimation and Inference in Threshold Predictive Regression Models with Locally Explosive Regressors