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Integer-valued stochastic volatility

Author

Listed:
  • Aknouche, Abdelhakim
  • Dimitrakopoulos, Stefanos
  • Touche, Nassim

Abstract

We propose a novel class of count time series models, the mixed Poisson integer-valued stochastic volatility models. The proposed specification, which can be considered as an integer-valued analogue of the discrete-time stochastic volatility model, encompasses a wide range of conditional distributions of counts. We study its probabilistic structure and develop an easily adaptable Markov chain Monte Carlo algorithm, based on the Griddy-Gibbs approach that can accommodate any conditional distribution that belongs to that class. We demonstrate that by considering the cases of Poisson and negative binomial distributions. The methodology is applied to simulated and real data.

Suggested Citation

  • Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos & Touche, Nassim, 2019. "Integer-valued stochastic volatility," MPRA Paper 91962, University Library of Munich, Germany, revised 04 Feb 2019.
  • Handle: RePEc:pra:mprapa:91962
    as

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    File URL: https://mpra.ub.uni-muenchen.de/91962/1/MPRA_paper_91962.pdf
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    References listed on IDEAS

    as
    1. Fokianos, Konstantinos & Rahbek, Anders & Tjøstheim, Dag, 2009. "Poisson Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1430-1439.
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    3. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    4. Cameron,A. Colin & Trivedi,Pravin K., 2013. "Regression Analysis of Count Data," Cambridge Books, Cambridge University Press, number 9781107667273.
    5. Ali Ahmad & Christian Francq, 2016. "Poisson QMLE of Count Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(3), pages 291-314, May.
    6. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    7. Robert Engle, 2002. "New frontiers for arch models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 425-446.
    8. Doukhan, Paul & Fokianos, Konstantinos & Tjøstheim, Dag, 2012. "On weak dependence conditions for Poisson autoregressions," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 942-948.
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    11. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
    12. Vasiliki Christou & Konstantinos Fokianos, 2014. "Quasi-Likelihood Inference For Negative Binomial Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(1), pages 55-78, January.
    13. Richard A. Davis & Rongning Wu, 2009. "A negative binomial model for time series of counts," Biometrika, Biometrika Trust, vol. 96(3), pages 735-749.
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    More about this item

    Keywords

    Griddy-Gibbs; Markov chain Monte Carlo; mixed Poisson parameter-driven models; stochastic volatility; Integer-valued GARCH.;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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