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

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

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 minutes intervals for five NYSE stocks from two industrial sectors. The estimated model accounts for all key dynamic and distributional features of the data. We find strong evidence of a common factor which we interpret as reflecting market-wide news. In contrast, sector-specific factors are found to be statistically insignifficant.
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Suggested Citation

  • Jung, Robert C. & Liesenfeld, Roman & Richard, Jean-François, 2011. "Dynamic Factor Models for Multivariate Count Data: An Application to Stock-Market Trading Activity," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 73-85.
  • Handle: RePEc:bes:jnlbes:v:29:i:1:y:2011:p:73-85
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    References listed on IDEAS

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    1. Jung, Robert C. & Kukuk, Martin & Liesenfeld, Roman, 2006. "Time series of count data: modeling, estimation and diagnostics," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2350-2364, December.
    2. Tauchen, George E & Pitts, Mark, 1983. "The Price Variability-Volume Relationship on Speculative Markets," Econometrica, Econometric Society, vol. 51(2), pages 485-505, March.
    3. Roman Liesenfeld & Robert C. Jung, 2000. "Stochastic volatility models: conditional normality versus heavy-tailed distributions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(2), pages 137-160.
    4. Liesenfeld, Roman, 2001. "A generalized bivariate mixture model for stock price volatility and trading volume," Journal of Econometrics, Elsevier, vol. 104(1), pages 141-178, August.
    5. Heinen, Andreas & Rengifo, Erick, 2007. "Multivariate autoregressive modeling of time series count data using copulas," Journal of Empirical Finance, Elsevier, vol. 14(4), pages 564-583, September.
    6. Wedel, Michel & Böckenholt, Ulf & Kamakura, Wagner A., 2003. "Factor models for multivariate count data," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 356-369, November.
    7. Richard, Jean-Francois & Zhang, Wei, 2007. "Efficient high-dimensional importance sampling," Journal of Econometrics, Elsevier, vol. 141(2), pages 1385-1411, December.
    8. Peter Neal & T. Subba Rao, 2007. "MCMC for Integer-Valued ARMA processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(1), pages 92-110, January.
    9. repec:pit:wpaper:321 is not listed on IDEAS
    10. HEINEN, Andréas, 2003. "Modelling time series count data: an autoregressive conditional Poisson model," CORE Discussion Papers 2003062, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Anat R. Admati, Paul Pfleiderer, 1988. "A Theory of Intraday Patterns: Volume and Price Variability," Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 3-40.
    12. Andersen, Torben G, 1996. " Return Volatility and Trading Volume: An Information Flow Interpretation of Stochastic Volatility," Journal of Finance, American Finance Association, vol. 51(1), pages 169-204, March.
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. repec:bla:irvfin:v:17:y:2017:i:3:p:479-490 is not listed on IDEAS
    4. 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.
    5. Brauning, Falk & Koopman, Siem Jan, 2016. "The dynamic factor network model with an application to global credit risk," Working Papers 16-13, Federal Reserve Bank of Boston.
    6. 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.
    7. 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.
    8. 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.
    9. Dimpfl, Thomas, 2014. "A note on cointegration of international stock market indices," International Review of Financial Analysis, Elsevier, vol. 33(C), pages 10-16.
    10. Kleppe, Tore Selland & Liesenfeld, Roman, 2014. "Efficient importance sampling in mixture frameworks," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 449-463.

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