Unifying Estimation and Inference for Linear Regression with Stationary and Integrated or Near-Integrated Variables.

The article focuses on developing a unified inference procedure for multiple linear regression models involving stationary (I(0)), integrated (I(1)), and nearly integrated (NI(1)) variables, addressing the challenge that least-squares estimators have different limiting distributions depending on the order of integration. To overcome difficulties in inference caused by unknown or mixed integration orders and heteroskedasticity, the authors propose a weighted estimation equation (WEE) method combined with a random weighting bootstrap approach, which consistently estimates the sampling distribution without requiring prior knowledge of the integration order or constant error variance. Simulation studies demonstrate that this method outperforms existing approaches under both constant and time-varying error variances. An empirical application to stock return predictability shows that accounting for endogeneity and uncertain integration orders using the proposed method provides stronger evidence of predictability compared to traditional methods.