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Auxiliary mixture sampling for parameter-driven models of time series of counts with applications to state space modelling

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  • Sylvia FrüHwirth-Schnatter
  • Helga Wagner

Abstract

We consider parameter-driven models of time series of counts, where the observations are assumed to arise from a Poisson distribution with a mean changing over time according to a latent process. Estimation of these models is carried out within a Bayesian framework using data augmentation and Markov chain Monte Carlo methods. We suggest a new auxiliary mixture sampler, which possesses a Gibbsian transition kernel, where we draw from full conditional distributions belonging to standard distribution families only. Emphasis lies on application to state space modelling of time series of counts, but we show that auxiliary mixture sampling may be applied to a wider range of parameter-driven models, including random-effects models and panel data models based on the Poisson distribution. Copyright 2006, Oxford University Press.

Suggested Citation

  • Sylvia FrüHwirth-Schnatter & Helga Wagner, 2006. "Auxiliary mixture sampling for parameter-driven models of time series of counts with applications to state space modelling," Biometrika, Biometrika Trust, vol. 93(4), pages 827-841, December.
  • Handle: RePEc:oup:biomet:v:93:y:2006:i:4:p:827-841
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    File URL: http://hdl.handle.net/10.1093/biomet/93.4.827
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    Citations

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    Cited by:

    1. Jouchi Nakajima & Tsuyoshi Kunihama & Yasuhiro Omori, 2015. "Bayesian Modeling of Dynamic Extreme Values: Extension of Generalized Extreme Value Distributions with Latent Stochastic Processes ," CIRJE F-Series CIRJE-F-952, CIRJE, Faculty of Economics, University of Tokyo.
    2. repec:tky:fseres:2014cf952 is not listed on IDEAS
    3. McCausland, William J., 2012. "The HESSIAN method: Highly efficient simulation smoothing, in a nutshell," Journal of Econometrics, Elsevier, vol. 168(2), pages 189-206.
    4. Frühwirth-Schnatter, Sylvia & Wagner, Helga, 2008. "Marginal likelihoods for non-Gaussian models using auxiliary mixture sampling," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4608-4624, June.
    5. 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.
    6. Nakajima, Jouchi & Kunihama, Tsuyoshi & Omori, Yasuhiro & Frühwirth-Schnatter, Sylvia, 2012. "Generalized extreme value distribution with time-dependence using the AR and MA models in state space form," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3241-3259.
    7. Samson B. Adebayo & Ludwig Fahrmeir & Christian Seiler & Christian Heumann, 2011. "Geoadditive Latent Variable Modeling of Count Data on Multiple Sexual Partnering in Nigeria," Biometrics, The International Biometric Society, vol. 67(2), pages 620-628, June.
    8. Kleppe, Tore Selland & Liesenfeld, Roman, 2014. "Efficient importance sampling in mixture frameworks," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 449-463.
    9. McCausland, William J. & Miller, Shirley & Pelletier, Denis, 2011. "Simulation smoothing for state-space models: A computational efficiency analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 199-212, January.
    10. Tsuyoshi Kunihama & Yasuhiro Omori & Zhengjun Zhang, 2012. "Efficient estimation and particle filter for max‐stable processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(1), pages 61-80, January.
    11. 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.
    12. Tsuyoshi Kunihama & Yasuhiro Omori & Zhengjun Zhang, 2010. "Bayesian Estimation and Particle Filter for Max-Stable Processes," CIRJE F-Series CIRJE-F-757, CIRJE, Faculty of Economics, University of Tokyo.
    13. Istvan Barra & Siem Jan Koopman & Agnieszka Borowska, 2016. "Bayesian Dynamic Modeling of High-Frequency Integer Price Changes," Tinbergen Institute Discussion Papers 16-028/III, Tinbergen Institute, revised 16 Feb 2018.
    14. Frühwirth-Schnatter, Sylvia & Wagner, Helga, 2010. "Stochastic model specification search for Gaussian and partial non-Gaussian state space models," Journal of Econometrics, Elsevier, vol. 154(1), pages 85-100, January.
    15. Chan, Joshua & Strachan, Rodney, 2012. "Estimation in Non-Linear Non-Gaussian State Space Models with Precision-Based Methods," MPRA Paper 39360, University Library of Munich, Germany.
    16. Feigin, Paul D. & Gould, Phillip & Martin, Gael M. & Snyder, Ralph D., 2008. "Feasible parameter regions for alternative discrete state space models," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2963-2970, December.

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