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Time Series of Count Data : Modelling and Estimation

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Author Info

  • Jung, Robert
  • Kukuk, Martin
  • Liesenfeld, Roman

Abstract

This paper compares various models for time series of counts which can account for discreetness, overdispersion and serial correlation. Besides observation- and parameter-driven models based upon corresponding conditional Poisson distributions, we also consider a dynamic ordered probit model as a flexible specification to capture the salient features of time series of counts. For all models, we present appropriate efficient estimation procedures. For parameter-driven specifications this requires Monte Carlo procedures like simulated Maximum likelihood or Markov Chain Monte-Carlo. The methods including corresponding diagnostic tests are illustrated with data on daily admissions for asthma to a single hospital. --

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File URL: http://econstor.eu/bitstream/10419/21996/1/EWP-2005-08.pdf
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Bibliographic Info

Paper provided by Christian-Albrechts-University of Kiel, Department of Economics in its series Economics Working Papers with number 2005,08.

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Date of creation: 2005
Date of revision:
Handle: RePEc:zbw:cauewp:3194

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Web page: http://www.wiso.uni-kiel.de/econ/
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Related research

Keywords: Efficient Importance Sampling; GLARMA; Markov Chain Monte-Carlo; Observation-driven model; Parameter-driven model; Ordered Probit;

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References

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  1. Tina Hviid Rydberg & Neil Shephard, 2002. "Dynamics of trade-by-trade price movements: decomposition and models," OFRC Working Papers Series 2002fe04, Oxford Financial Research Centre.
  2. Heinen, Andreas, 2003. "Modelling Time Series Count Data: An Autoregressive Conditional Poisson Model," MPRA Paper 8113, University Library of Munich, Germany.
  3. Richard A. Davis, 2003. "Observation-driven models for Poisson counts," Biometrika, Biometrika Trust, vol. 90(4), pages 777-790, December.
  4. Shephard, N. & Pitt, M.K., 1995. "Likelihood Analysis of Non-Gaussian Parameter-Driven Models," Economics Papers 108, Economics Group, Nuffield College, University of Oxford.
  5. Sangjoon Kim & Neil Shephard, 1994. "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers 3., Economics Group, Nuffield College, University of Oxford.
  6. Luc Bauwens & Michel Lubrano, 1998. "Bayesian inference on GARCH models using the Gibbs sampler," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages C23-C46.
  7. Chib, Siddhartha & Winkelmann, Rainer, 2001. "Markov Chain Monte Carlo Analysis of Correlated Count Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 428-35, October.
  8. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  9. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
  10. Hausman, Jerry A. & Lo, Andrew W. & MacKinlay, A. Craig, 1992. "An ordered probit analysis of transaction stock prices," Journal of Financial Economics, Elsevier, vol. 31(3), pages 319-379, June.
  11. Liesenfeld, Roman & Richard, Jean-Francois, 2003. "Univariate and multivariate stochastic volatility models: estimation and diagnostics," Journal of Empirical Finance, Elsevier, vol. 10(4), pages 505-531, September.
  12. Danielsson, J & Richard, J-F, 1993. "Accelerated Gaussian Importance Sampler with Application to Dynamic Latent Variable Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S153-73, Suppl. De.
  13. Roman Liesenfeld & Ingmar Nolte & Winfried Pohlmeier, 2006. "Modelling financial transaction price movements: a dynamic integer count data model," Empirical Economics, Springer, vol. 30(4), pages 795-825, January.
  14. Neil Shephard, 1995. "Generalized linear autoregressions," Economics Papers 8., Economics Group, Nuffield College, University of Oxford.
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Citations

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Cited by:
  1. Felbermayr, Gabriel & Toubal, Farid, 2006. "Cultural proximity and trade," Tübinger Diskussionsbeiträge 305, University of Tübingen, School of Business and Economics.
  2. Carvalho, Alexandre X. & Tanner, Martin A., 2007. "Modelling nonlinear count time series with local mixtures of Poisson autoregressions," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5266-5294, July.
  3. Maier, Ramona & Merz, Michael, 2008. "Credibility theory and filter theory in discrete and continuous time," Tübinger Diskussionsbeiträge 318, University of Tübingen, School of Business and Economics.
  4. Frontczak, Robert, 2009. "Valuing options in Heston's stochastic volatility model: Another analytical approach," Tübinger Diskussionsbeiträge 326, University of Tübingen, School of Business and Economics.
  5. Frontczak, Robert & Schöbel, Rainer, 2009. "On modified Mellin transforms, Gauss-Laguerre quadrature, and the valuation of American call options," Tübinger Diskussionsbeiträge 320, University of Tübingen, School of Business and Economics.
  6. Heger, Diana & Zaby, Alexandra K., 2009. "The propensity to patent with horizontally differentiated products: An empirical investigation," Tübinger Diskussionsbeiträge 324, University of Tübingen, School of Business and Economics.
  7. Frontczak, Robert & Schöbel, Rainer, 2008. "Pricing American options with Mellin transforms," Tübinger Diskussionsbeiträge 319, University of Tübingen, School of Business and Economics.
  8. Dymke, Björn M. & Walter, Andreas, 2006. "Insider trading in Germany: Do corporate insiders exploit inside information?," Tübinger Diskussionsbeiträge 309, University of Tübingen, School of Business and Economics.
  9. Mailu, Stephen & Lukibisi, Barasa & Waithaka, Michael, 2011. "Application of various count models: Sahiwal demand from Naivasha," MPRA Paper 32074, University Library of Munich, Germany, revised 06 Jul 2011.
  10. Yalcin, Erdal, 2007. "The proximity-concentration trade-off in a dynamic framework," Tübinger Diskussionsbeiträge 312, University of Tübingen, School of Business and Economics.
  11. Rostek, Stefan & Schöbel, Rainer, 2006. "Risk preference based option pricing in a fractional Brownian market," Tübinger Diskussionsbeiträge 299, University of Tübingen, School of Business and Economics.
  12. Heger, Diana & Zaby, Alexandra K., 2009. "The propensity to patent with vertically differentiated products: An empirical investigation," Tübinger Diskussionsbeiträge 325, University of Tübingen, School of Business and Economics.
  13. Zaby, Alexandra K., 2009. "The propensity to patent in oligopolistic markets," Tübinger Diskussionsbeiträge 323, University of Tübingen, School of Business and Economics.
  14. Andres Pereyra & Elías Rubinstein & Marcelo Pérez, 2008. "Tasa generadora de viajes para el puerto de Montevideo. Una propuesta metodológica," Documentos de Trabajo (working papers) 2108, Department of Economics - dECON.
  15. Schüle, Tobias, 2006. "Creditor coordination with social learning and endogenous timing of credit decisions," Tübinger Diskussionsbeiträge 307, University of Tübingen, School of Business and Economics.
  16. Hager, Svenja & Schöbel, Rainer, 2006. "Deriving the dependence structure of portfolio credit derivatives using evolutionary algorithms," Tübinger Diskussionsbeiträge 300, University of Tübingen, School of Business and Economics.
  17. Ralph D. Snyder & Gael M. Martin & Phillip Gould & Paul D. Feigin, 2007. "An Assessment of Alternative State Space Models for Count Time Series," Monash Econometrics and Business Statistics Working Papers 4/07, Monash University, Department of Econometrics and Business Statistics.
  18. Brandes, Julia & Schüle, Tobias, 2007. "IMF's assistance: Devil's kiss or guardian angel?," Tübinger Diskussionsbeiträge 310, University of Tübingen, School of Business and Economics.

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