IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2409.08354.html
   My bibliography  Save this paper

Bayesian Dynamic Factor Models for High-dimensional Matrix-valued Time Series

Author

Listed:
  • Wei Zhang

Abstract

High-dimensional matrix-valued time series are of significant interest in economics and finance, with prominent examples including cross region macroeconomic panels and firms' financial data panels. We introduce a class of Bayesian matrix dynamic factor models that utilize matrix structures to identify more interpretable factor patterns and factor impacts. Our model accommodates time-varying volatility, adjusts for outliers, and allows cross-sectional correlations in the idiosyncratic components. To determine the dimension of the factor matrix, we employ an importance-sampling estimator based on the cross-entropy method to estimate marginal likelihoods. Through a series of Monte Carlo experiments, we show the properties of the factor estimators and the performance of the marginal likelihood estimator in correctly identifying the true dimensions of the factor matrices. Applying our model to a macroeconomic dataset and a financial dataset, we demonstrate its ability in unveiling interesting features within matrix-valued time series.

Suggested Citation

  • Wei Zhang, 2024. "Bayesian Dynamic Factor Models for High-dimensional Matrix-valued Time Series," Papers 2409.08354, arXiv.org.
    • Handle: RePEc:arx:papers:2409.08354
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2409.08354
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Timothy Cogley & Thomas J. Sargent, 2005. "Drift and Volatilities: Monetary Policies and Outcomes in the Post WWII U.S," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(2), pages 262-302, April.
    2. Lucia Alessi & Mark Kerssenfischer, 2019. "The response of asset prices to monetary policy shocks: Stronger than thought," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(5), pages 661-672, August.
    3. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2006. "Analysis of high dimensional multivariate stochastic volatility models," Journal of Econometrics, Elsevier, vol. 134(2), pages 341-371, October.
    4. Alexei Onatski, 2010. "Determining the Number of Factors from Empirical Distribution of Eigenvalues," The Review of Economics and Statistics, MIT Press, vol. 92(4), pages 1004-1016, November.
    5. Chen, Rong & Xiao, Han & Yang, Dan, 2021. "Autoregressive models for matrix-valued time series," Journal of Econometrics, Elsevier, vol. 222(1), pages 539-560.
    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. Zhang, Yixiao & Yu, Cindy L. & Li, Haitao, 2022. "Nowcasting GDP Using Dynamic Factor Model with Unknown Number of Factors and Stochastic Volatility: A Bayesian Approach," Econometrics and Statistics, Elsevier, vol. 24(C), pages 75-93.
    2. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2016. "Common Drifting Volatility in Large Bayesian VARs," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 375-390, July.
    3. Chan, Joshua C.C., 2013. "Moving average stochastic volatility models with application to inflation forecast," Journal of Econometrics, Elsevier, vol. 176(2), pages 162-172.
    4. Koop, Gary & Korobilis, Dimitris, 2010. "Bayesian Multivariate Time Series Methods for Empirical Macroeconomics," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(4), pages 267-358, July.
    5. Stock, J.H. & Watson, M.W., 2016. "Dynamic Factor Models, Factor-Augmented Vector Autoregressions, and Structural Vector Autoregressions in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 415-525, Elsevier.
    6. Sung Hoon Choi & Donggyu Kim, 2023. "Large Global Volatility Matrix Analysis Based on Observation Structural Information," Papers 2305.01464, arXiv.org, revised Feb 2024.
    7. Joshua C. C. Chan & Liana Jacobi & Dan Zhu, 2022. "An automated prior robustness analysis in Bayesian model comparison," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(3), pages 583-602, April.
    8. Rodríguez, Gabriel & Vassallo, Renato & Castillo B., Paul, 2023. "Effects of external shocks on macroeconomic fluctuations in Pacific Alliance countries," Economic Modelling, Elsevier, vol. 124(C).
    9. Gribisch, Bastian, 2013. "A latent dynamic factor approach to forecasting multivariate stock market volatility," VfS Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79823, Verein für Socialpolitik / German Economic Association.
    10. Legrand, Romain, 2018. "Time-Varying Vector Autoregressions: Efficient Estimation, Random Inertia and Random Mean," MPRA Paper 88925, University Library of Munich, Germany.
    11. Joshua Chan & Eric Eisenstat & Xuewen Yu, 2022. "Large Bayesian VARs with Factor Stochastic Volatility: Identification, Order Invariance and Structural Analysis," Papers 2207.03988, arXiv.org.
    12. Gong, Xiao-Li & Liu, Xi-Hua & Xiong, Xiong & Zhuang, Xin-Tian, 2018. "Modeling volatility dynamics using non-Gaussian stochastic volatility model based on band matrix routine," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 193-201.
    13. Joshua C.C. Chan & Angelia L. Grant, 2014. "Issues in Comparing Stochastic Volatility Models Using the Deviance Information Criterion," CAMA Working Papers 2014-51, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    14. Ping Wu & Gary Koop, 2022. "Fast, Order-Invariant Bayesian Inference in VARs using the Eigendecomposition of the Error Covariance Matrix," Working Papers 2310, University of Strathclyde Business School, Department of Economics.
    15. Gabriel Rodríguez & Renato Vassallo, 2022. "Time Evolution of External Shocks on Macroeconomic Fluctuations in Pacific Alliance Countries: Empirical Application using TVP-VAR-SV Models," Documentos de Trabajo / Working Papers 2022-508, Departamento de Economía - Pontificia Universidad Católica del Perú.
    16. Zhou, Xiaocong & Nakajima, Jouchi & West, Mike, 2014. "Bayesian forecasting and portfolio decisions using dynamic dependent sparse factor models," International Journal of Forecasting, Elsevier, vol. 30(4), pages 963-980.
    17. Chan, Joshua C.C., 2023. "Comparing stochastic volatility specifications for large Bayesian VARs," Journal of Econometrics, Elsevier, vol. 235(2), pages 1419-1446.
    18. Soojin Jo & Rodrigo Sekkel, 2019. "Macroeconomic Uncertainty Through the Lens of Professional Forecasters," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(3), pages 436-446, July.
    19. Didier Nibbering & Richard Paap & Michel van der Wel, 2016. "A Bayesian Infinite Hidden Markov Vector Autoregressive Model," Tinbergen Institute Discussion Papers 16-107/III, Tinbergen Institute, revised 13 Oct 2017.
    20. Pooyan Amir-Ahmadi & Christian Matthes & Mu-Chun Wang, 2016. "Choosing Prior Hyperparameters," Working Paper 16-9, Federal Reserve Bank of Richmond.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2409.08354. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.