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

Harrison Katz (), Liz Medina and Robert E. Weiss ()
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Harrison Katz: Department of Statistics & Data Science, University of California, Los Angeles, 8125 Math Sciences Building, Los Angeles, CA 90095-1554, USA
Liz Medina: Data Science—Forecasting, Airbnb, Inc., 888 Brannan Street, San Francisco, CA 94103, USA
Robert E. Weiss: Department of Biostatistics, Fielding School of Public Health, University of California, Los Angeles, 650 Charles E. Young Dr. South, Los Angeles, CA 90095-1772, USA

Forecasting, 2025, vol. 7, issue 3, 1-19

Abstract: 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.

Keywords: Bayesian Dirichlet ARMA; compositional time series; forecasting; sensitivity analysis; shrinkage priors; S&P 500 sectors; Stan (search for similar items in EconPapers)
JEL-codes: A1 B4 C0 C1 C2 C3 C4 C5 C8 M0 Q2 Q3 Q4 (search for similar items in EconPapers)
Date: 2025
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