IDEAS home Printed from https://ideas.repec.org/a/gam/jforec/v7y2025i3p32-d1684138.html
   My bibliography  Save this article

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

Author

Listed:
  • Harrison Katz

    (Department of Statistics & Data Science, University of California, Los Angeles, 8125 Math Sciences Building, Los Angeles, CA 90095-1554, USA
    Data Science—Forecasting, Airbnb, Inc., 888 Brannan Street, San Francisco, CA 94103, 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)

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.

Suggested Citation

  • Harrison Katz & Liz Medina & Robert E. Weiss, 2025. "Sensitivity Analysis of Priors in the Bayesian Dirichlet Auto-Regressive Moving Average Model," Forecasting, MDPI, vol. 7(3), pages 1-19, June.
    • Handle: RePEc:gam:jforec:v:7:y:2025:i:3:p:32-:d:1684138
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2571-9394/7/3/32/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2571-9394/7/3/32/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Carlos M. Carvalho & Nicholas G. Polson & James G. Scott, 2010. "The horseshoe estimator for sparse signals," Biometrika, Biometrika Trust, vol. 97(2), pages 465-480.
    2. Lipsmeyer, Christine S. & Philips, Andrew Q. & Rutherford, Amanda & Whitten, Guy D., 2019. "Comparing Dynamic Pies: A Strategy for Modeling Compositional Variables in Time and Space," Political Science Research and Methods, Cambridge University Press, vol. 7(3), pages 523-540, July.
    3. Seitebaleng Makgai & Andriette Bekker & Mohammad Arashi, 2021. "Compositional Data Modeling through Dirichlet Innovations," Mathematics, MDPI, vol. 9(19), pages 1-18, October.
    4. Boonen, Tim J. & Guillen, Montserrat & Santolino, Miguel, 2019. "Forecasting compositional risk allocations," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 79-86.
    5. Bitto, Angela & Frühwirth-Schnatter, Sylvia, 2019. "Achieving shrinkage in a time-varying parameter model framework," Journal of Econometrics, Elsevier, vol. 210(1), pages 75-97.
    6. Zheng, Tingguo & Chen, Rong, 2017. "Dirichlet ARMA models for compositional time series," Journal of Multivariate Analysis, Elsevier, vol. 158(C), pages 31-46.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hauzenberger, Niko, 2021. "Flexible Mixture Priors for Large Time-varying Parameter Models," Econometrics and Statistics, Elsevier, vol. 20(C), pages 87-108.
    2. Hu, Guanyu, 2021. "Spatially varying sparsity in dynamic regression models," Econometrics and Statistics, Elsevier, vol. 17(C), pages 23-34.
    3. Kohns, David & Bhattacharjee, Arnab, 2023. "Nowcasting growth using Google Trends data: A Bayesian Structural Time Series model," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1384-1412.
    4. Annalisa Cadonna & Sylvia Frühwirth-Schnatter & Peter Knaus, 2020. "Triple the Gamma—A Unifying Shrinkage Prior for Variance and Variable Selection in Sparse State Space and TVP Models," Econometrics, MDPI, vol. 8(2), pages 1-36, May.
    5. Yu Bai & Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2022. "Macroeconomic forecasting in a multi‐country context," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(6), pages 1230-1255, September.
    6. Peter Knaus & Sylvia Fruhwirth-Schnatter, 2023. "The Dynamic Triple Gamma Prior as a Shrinkage Process Prior for Time-Varying Parameter Models," Papers 2312.10487, arXiv.org, revised Jan 2025.
    7. Juan David Vega Baquero & Miguel Santolino, 2021. ""Too big to fail? An analysis of the Colombian banking system through compositional data"," IREA Working Papers 202111, University of Barcelona, Research Institute of Applied Economics, revised Apr 2021.
    8. Katz, Harrison & Brusch, Kai Thomas & Weiss, Robert E., 2024. "A Bayesian Dirichlet auto-regressive moving average model for forecasting lead times," International Journal of Forecasting, Elsevier, vol. 40(4), pages 1556-1567.
    9. Dimitris Korobilis & Kenichi Shimizu, 2022. "Bayesian Approaches to Shrinkage and Sparse Estimation," Foundations and Trends(R) in Econometrics, now publishers, vol. 11(4), pages 230-354, June.
    10. Uddin, Md Nazir & Gaskins, Jeremy T., 2023. "Shared Bayesian variable shrinkage in multinomial logistic regression," Computational Statistics & Data Analysis, Elsevier, vol. 177(C).
    11. Luis Gruber & Gregor Kastner, 2022. "Forecasting macroeconomic data with Bayesian VARs: Sparse or dense? It depends!," Papers 2206.04902, arXiv.org, revised Feb 2025.
    12. Smith, Michael Stanley, 2023. "Implicit Copulas: An Overview," Econometrics and Statistics, Elsevier, vol. 28(C), pages 81-104.
    13. Sylvia Fruhwirth-Schnatter & Peter Knaus, 2022. "Sparse Bayesian State-Space and Time-Varying Parameter Models," Papers 2207.12147, arXiv.org.
    14. Niko Hauzenberger, 2020. "Flexible Mixture Priors for Large Time-varying Parameter Models," Papers 2006.10088, arXiv.org, revised Nov 2020.
    15. Michael Stanley Smith, 2021. "Implicit Copulas: An Overview," Papers 2109.04718, arXiv.org.
    16. Vega Baquero, Juan David & Santolino, Miguel, 2022. "Too big to fail? An analysis of the Colombian banking system through compositional data," Latin American Journal of Central Banking (previously Monetaria), Elsevier, vol. 3(2).
    17. Zhongfang He, 2024. "Locally time-varying parameter regression," Econometric Reviews, Taylor & Francis Journals, vol. 43(5), pages 269-300, May.
    18. Annalisa Cadonna & Sylvia Fruhwirth-Schnatter & Peter Knaus, 2019. "Triple the gamma -- A unifying shrinkage prior for variance and variable selection in sparse state space and TVP models," Papers 1912.03100, arXiv.org.
    19. Mauro Bernardi & Daniele Bianchi & Nicolas Bianco, 2022. "Variational inference for large Bayesian vector autoregressions," Papers 2202.12644, arXiv.org, revised Jun 2023.
    20. Hauzenberger, Niko & Huber, Florian & Klieber, Karin & Marcellino, Massimiliano, 2025. "Bayesian neural networks for macroeconomic analysis," Journal of Econometrics, Elsevier, vol. 249(PC).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jforec:v:7:y:2025:i:3:p:32-:d:1684138. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.