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MCMC for Integer‐Valued ARMA processes

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  • Peter Neal
  • T. Subba Rao

Abstract

. The classical statistical inference for integer‐valued time‐series has primarily been restricted to the integer‐valued autoregressive (INAR) process. Markov chain Monte Carlo (MCMC) methods have been shown to be a useful tool in many branches of statistics and is particularly well suited to integer‐valued time‐series where statistical inference is greatly assisted by data augmentation. Thus in this article, we outline an efficient MCMC algorithm for a wide class of integer‐valued autoregressive moving‐average (INARMA) processes. Furthermore, we consider noise corrupted integer‐valued processes and also models with change points. Finally, in order to assess the MCMC algorithms inferential and predictive capabilities we use a range of simulated and real data sets.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:28:y:2007:i:1:p:92-110
    DOI: 10.1111/j.1467-9892.2006.00500.x
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    Cited by:

    1. 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.
    2. Yang, Kai & Yu, Xinyang & Zhang, Qingqing & Dong, Xiaogang, 2022. "On MCMC sampling in self-exciting integer-valued threshold time series models," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    3. Lennon, Hannah & Yuan, Jingsong, 2019. "Estimation of a digitised Gaussian ARMA model by Monte Carlo Expectation Maximisation," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 277-284.
    4. Alzahrani, Naif & Neal, Peter & Spencer, Simon E.F. & McKinley, Trevelyan J. & Touloupou, Panayiota, 2018. "Model selection for time series of count data," Computational Statistics & Data Analysis, Elsevier, vol. 122(C), pages 33-44.
    5. Frazier, David T. & Maneesoonthorn, Worapree & Martin, Gael M. & McCabe, Brendan P.M., 2019. "Approximate Bayesian forecasting," International Journal of Forecasting, Elsevier, vol. 35(2), pages 521-539.
    6. Xinyang Wang & Dehui Wang & Kai Yang, 2021. "Integer-valued time series model order shrinkage and selection via penalized quasi-likelihood approach," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 713-750, July.
    7. Mohammadipour, Maryam & Boylan, John E., 2012. "Forecast horizon aggregation in integer autoregressive moving average (INARMA) models," Omega, Elsevier, vol. 40(6), pages 703-712.
    8. Víctor Enciso‐Mora & Peter Neal & T. Subba Rao, 2009. "Efficient order selection algorithms for integer‐valued ARMA processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 1-18, January.
    9. Schatz, Michael & Wheatley, Spencer & Sornette, Didier, 2022. "The ARMA Point Process and its Estimation," Econometrics and Statistics, Elsevier, vol. 24(C), pages 164-182.
    10. Christian H. Weiß & Martin H.-J. M. Feld & Naushad Mamode Khan & Yuvraj Sunecher, 2019. "INARMA Modeling of Count Time Series," Stats, MDPI, vol. 2(2), pages 1-37, June.
    11. Federico Bassetti & Giulia Carallo & Roberto Casarin, 2022. "First-order integer-valued autoregressive processes with Generalized Katz innovations," Papers 2202.02029, arXiv.org.

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