Bayesian Estimation and Forecasting of Constrained Spatial Panel Interval‐Valued Autoregressive Models

ABSTRACT

Spatiotemporal interval‐valued data have become increasingly important for modeling uncertainty in complex systems, and related statistical methods and forecasting tools remain underdeveloped. This paper proposes a constrained spatial panel interval‐valued autoregressive model, which ensures mathematical coherence by applying a Mills ratio–based correction and captures the dependence between lower and upper bounds. A Bayesian estimation incorporating prior information is then developed, and a corresponding Metropolis‐within‐Gibbs sampling algorithm is constructed. This algorithm provides a computationally tractable simulation‐based framework for estimating the parameters of the proposed model. Monte Carlo simulations show that the proposed method performs favorably relative to several benchmark approaches in parameter estimation, interval fitting, and forecasting. Applications to air quality and housing price data further demonstrate its ability to model spatiotemporal dependence and interval uncertainty effectively. The results highlight the practical value of the proposed model for analyzing environmental and economic systems characterized by uncertainty.