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INARMA Modeling of Count Time Series

Author

Listed:
  • Christian H. Weiß

    (Department of Mathematics and Statistics, Helmut Schmidt University, 22043 Hamburg, Germany)

  • Martin H.-J. M. Feld

    (Department of Mathematics and Statistics, Helmut Schmidt University, 22043 Hamburg, Germany)

  • Naushad Mamode Khan

    (Department of Economics and Statistics, University of Mauritius, Reduit 80837, Mauritius)

  • Yuvraj Sunecher

    (School of Business, Management and Finance, University of Technology, La Tour Koenig 11134, Mauritius)

Abstract

While most of the literature about INARMA models (integer-valued autoregressive moving-average) concentrates on the purely autoregressive INAR models, we consider INARMA models that also include a moving-average part. We study moment properties and show how to efficiently implement maximum likelihood estimation. We analyze the estimation performance and consider the topic of model selection. We also analyze the consequences of choosing an inadequate model for the given count process. Two real-data examples are presented for illustration.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jstats:v:2:y:2019:i:2:p:22-320:d:236899
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    References listed on IDEAS

    as
    1. Brännäs, Kurt & Quoreshi, Shahiduzzaman, 2004. "Integer-Valued Moving Average Modelling of the Number of Transactions in Stocks," Umeå Economic Studies 637, Umeå University, Department of Economics.
    2. 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.
    3. R. K. Freeland & B. P. M. McCabe, 2004. "Analysis of low count time series data by poisson autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 701-722, September.
    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. Kurt Brännäs & Andreia Hall, 2001. "Estimation in integer‐valued moving average models," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 17(3), pages 277-291, July.
    6. Ruey S. Tsay, 1992. "Model Checking Via Parametric Bootstraps in Time Series Analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(1), pages 1-15, March.
    7. 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.
    Full references (including those not matched with items on IDEAS)

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