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Efficient order selection algorithms for integer‐valued ARMA processes

Author

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  • Víctor Enciso‐Mora
  • Peter Neal
  • T. Subba Rao

Abstract

. We consider the problem of model (order) selection for integer‐valued autoregressive moving‐average (INARMA) processes. A very efficient reversible jump Markov chain Monte Carlo (RJMCMC) algorithm is constructed for moving between INARMA processes of different orders. An alternative in the form of the EM algorithm is given for determining the order of an integer‐valued autoregressive (INAR) process. Both algorithms are successfully applied to both simulated and real data sets.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:30:y:2009:i:1:p:1-18
    DOI: 10.1111/j.1467-9892.2008.00592.x
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    References listed on IDEAS

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    1. Freeland, R. K. & McCabe, B. P. M., 2004. "Forecasting discrete valued low count time series," International Journal of Forecasting, Elsevier, vol. 20(3), pages 427-434.
    2. 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.
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    7. McCabe, B.P.M. & Martin, G.M., 2005. "Bayesian predictions of low count time series," International Journal of Forecasting, Elsevier, vol. 21(2), pages 315-330.
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    Cited by:

    1. Schatz, Michael & Wheatley, Spencer & Sornette, Didier, 2022. "The ARMA Point Process and its Estimation," Econometrics and Statistics, Elsevier, vol. 24(C), pages 164-182.
    2. 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.
    3. Barczy, M. & Ispány, M. & Pap, G., 2011. "Asymptotic behavior of unstable INAR(p) processes," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 583-608, March.
    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. Chigozie E. Utazi, 2017. "Bayesian Single Changepoint Estimation in a Parameter-driven Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(3), pages 765-779, September.
    6. Kaizhi Yu & Hong Zou & Daimin Shi, 2013. "Nonstationary INAR(1) Process with qth‐Order Autocorrelation Innovation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    7. Kobayashi, Genya, 2014. "A transdimensional approximate Bayesian computation using the pseudo-marginal approach for model choice," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 167-183.
    8. Wagner Barreto‐Souza & Hernando Ombao, 2022. "The negative binomial process: A tractable model with composite likelihood‐based inference," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 568-592, June.

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