A Bayesian Hierarchical Semiparametric Approach to Modeling Interval-Valued Panel Data

This study proposes a Bayesian Hierarchical Semiparametric Center and Range (BHS-CRM) model to address nonlinearity and heterogeneity in interval-valued panel data. By incorporating Bayesian penalized B-splines (P-splines) into a hierarchical random effects structure, the proposed method utilizes a parallel dual-component framework to separately capture dynamic central tendencies and variability. Simulation studies demonstrate the model’s robust performance, particularly in capturing nonlinear dynamics under high-noise conditions. Empirically, the model characterizes nonlinear temperature patterns in China’s Carbon Emission Trading Scheme (ETS) and achieves competitive out-of-sample predictive accuracy.