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Dynamic Factor Models for Multivariate Count Data: An Application to Stock-Market Trading Activity

Author

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  • Robert C. Jung
  • Roman Liesenfeld
  • Jean-François Richard

Abstract

We propose a dynamic factor model for the analysis of multivariate time series count data. Our model allows for idiosyncratic as well as common serially correlated latent factors in order to account for potentially complex dynamic interdependence between series of counts. The model is estimated under alternative count distributions (Poisson and negative binomial). Maximum likelihood estimation requires high-dimensional numerical integration in order to marginalize the joint distribution with respect to the unobserved dynamic factors. We rely upon the Monte Carlo integration procedure known as efficient importance sampling, which produces fast and numerically accurate estimates of the likelihood function. The model is applied to time series data consisting of numbers of trades in 5-min intervals for five New York Stock Exchange (NYSE) stocks from two industrial sectors. The estimated model provides a good parsimonious representation of the contemporaneous correlation across the individual stocks and their serial correlation. It also provides strong evidence of a common factor, which we interpret as reflecting market-wide news.

Suggested Citation

  • Robert C. Jung & Roman Liesenfeld & Jean-François Richard, 2011. "Dynamic Factor Models for Multivariate Count Data: An Application to Stock-Market Trading Activity," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 73-85, January.
    • Handle: RePEc:taf:jnlbes:v:29:y:2011:i:1:p:73-85
    DOI: 10.1198/jbes.2009.08212
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    Cited by:

    1. Jean-François Richard, 2015. "Likelihood Evaluation of High-Dimensional Spatial Latent Gaussian Models with Non-Gaussian Response Variables," Working Paper 5778, Department of Economics, University of Pittsburgh.
    2. Fokianos, Konstantinos, 2024. "Multivariate Count Time Series Modelling," Econometrics and Statistics, Elsevier, vol. 31(C), pages 100-116.
    3. Rainer Baule & Bart Frijns & Sebastian Schlie, 2024. "Feedback Trading: The Intraday Case of Retail Derivatives," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(9), pages 1487-1507, September.
    4. Dag Tjøstheim, 2012. "Some recent theory for autoregressive count time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 413-438, September.
    5. Siem Jan Koopman & Rutger Lit & Thuy Minh Nguyen, 2012. "Fast Efficient Importance Sampling by State Space Methods," Tinbergen Institute Discussion Papers 12-008/4, Tinbergen Institute, revised 16 Oct 2014.
    6. Falk Bräuning & Siem Jan Koopman, 2016. "The Dynamic Factor Network Model with an Application to Global Credit-Risk," Tinbergen Institute Discussion Papers 16-105/III, Tinbergen Institute.
    7. Dimpfl, Thomas, 2014. "A note on cointegration of international stock market indices," International Review of Financial Analysis, Elsevier, vol. 33(C), pages 10-16.
    8. Marina Gomtsyan & Céline Lévy-Leduc & Sarah Ouadah & Laure Sansonnet & Christophe Bailly & Loïc Rajjou, 2025. "Variable selection in sparse multivariate GLARMA models: application to germination control by environment," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 34(2), pages 291-324, May.
    9. Catania, Leopoldo & Di Mari, Roberto, 2021. "Hierarchical Markov-switching models for multivariate integer-valued time-series," Journal of Econometrics, Elsevier, vol. 221(1), pages 118-137.
    10. Luiza S. C. Piancastelli & Wagner Barreto‐Souza & Hernando Ombao, 2023. "Flexible bivariate INGARCH process with a broad range of contemporaneous correlation," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(2), pages 206-222, March.
    11. Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos, 2020. "On an integer-valued stochastic intensity model for time series of counts," MPRA Paper 105406, University Library of Munich, Germany.
    12. Alessio Farcomeni & Monia Ranalli & Sara Viviani, 2021. "Dimension reduction for longitudinal multivariate data by optimizing class separation of projected latent Markov models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 462-480, June.
    13. Kleppe, Tore Selland & Liesenfeld, Roman, 2011. "Efficient high-dimensional importance sampling in mixture frameworks," Economics Working Papers 2011-11, Christian-Albrechts-University of Kiel, Department of Economics.
    14. Kleppe, Tore Selland & Liesenfeld, Roman, 2014. "Efficient importance sampling in mixture frameworks," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 449-463.
    15. Serda S. Öztürk & Thanasis Stengos, 2017. "A Multivariate Stochastic Volatility Model Applied to a Panel of S&P500 Stocks in Different Industries," International Review of Finance, International Review of Finance Ltd., vol. 17(3), pages 479-490, September.
    16. Fokianos, Konstantinos & Fried, Roland & Kharin, Yuriy & Voloshko, Valeriy, 2022. "Statistical analysis of multivariate discrete-valued time series," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    17. Li, Qi & Lian, Heng & Zhu, Fukang, 2016. "Robust closed-form estimators for the integer-valued GARCH (1,1) model," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 209-225.
    18. Skaug, Hans J. & Yu, Jun, 2014. "A flexible and automated likelihood based framework for inference in stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 642-654.
    19. Norets, Andriy & Pelenis, Justinas, 2022. "Adaptive Bayesian estimation of conditional discrete-continuous distributions with an application to stock market trading activity," Journal of Econometrics, Elsevier, vol. 230(1), pages 62-82.
    20. Ahn, Jae Youn & Jeong, Himchan & Lu, Yang & Wüthrich, Mario V., 2025. "An observation-driven state-space count model for experience rating," Insurance: Mathematics and Economics, Elsevier, vol. 125(C).
    21. Jian Pei & Yang Lu & Fukang Zhu, 2025. "Mixed causal-noncausal count process," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 34(2), pages 325-360, June.
    22. Bräuning, Falk & Koopman, Siem Jan, 2020. "The dynamic factor network model with an application to international trade," Journal of Econometrics, Elsevier, vol. 216(2), pages 494-515.
    23. Younghoon Kim & Marie-Christine Duker & Zachary F. Fisher & Vladas Pipiras, 2023. "Latent Gaussian dynamic factor modeling and forecasting for multivariate count time series," Papers 2307.10454, arXiv.org, revised Apr 2025.

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