Bivariate Bayesian regression method for fixed effects panel interval-valued data models

Despite the growing body of literature on panel interval-valued data models, there is a scarcity of methods available for panel interval-valued data regression. This article extends the fixed effects panel interval-valued data center and range model as well as the Min-Max model to a Bayesian framework while considering the correlation between upper and lower bounds of intervals reflected in the covariance matrix. We explore two scenarios where the covariance matrix is either known or unknown. Additionally, we demonstrate that our proposed bivariate Bayesian regression method can also be applied to panel interval-valued data models with uncorrelated interval bounds of idiosyncratic error. Synthetic and real data applications validate that our proposed method yields superior fitting and forecasting performances.