Sensitivity Analysis of Priors in the Bayesian Dirichlet Auto-Regressive Moving Average Model

We examine how prior specification affects the Bayesian Dirichlet Auto-Regressive Moving Average (B-DARMA) model for compositional time series. Through three simulation scenarios—correct specification, overfitting, and underfitting—we compare five priors: informative, horseshoe, Laplace, mixture of normals, and hierarchical. Under correct model specification, all priors perform similarly, although the horseshoe and hierarchical priors produce slightly lower bias. When the model overfits, strong shrinkage—particularly from the horseshoe prior—proves advantageous. However, none of the priors can compensate for model misspecification if key VAR/VMA terms are omitted. We apply B-DARMA to daily S&P 500 sector trading data, using a large-lag model to demonstrate overparameterization risks. Shrinkage priors effectively mitigate spurious complexity, whereas weakly informative priors inflate errors in volatile sectors. These findings highlight the critical role of carefully selecting priors and managing model complexity in compositional time-series analysis, particularly in high-dimensional settings.