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An INAR(1) model with Poisson-Lindley innovations

Author

Listed:
  • Tito Lívio

    (Universidade Federal do Piauí)

  • Naushad Mamode Khan

    (University of Mauritius)

  • Marcelo Bourguignon

    (Universidade Federal do Rio Grande do Norte)

  • Hassan S. Bakouch

    (Tanta University)

Abstract

Real count data time series often show the phenomenon of the overdispersion. In this paper, we introduce a first order non-negative integer valued autoregressive process with Poisson-Lindley innovations based on the binomial thinning operator. The new model is particularly suitable for time series of counts exhibiting overdispersion and therefore competes against others recently established. The main properties of the model are derived. The methods of conditional least squares, Yule-Walker and conditional maximum likelihood are used for estimating the parameters. The proposed model is also applied to a weekly sales of soap product data series.

Suggested Citation

  • Tito Lívio & Naushad Mamode Khan & Marcelo Bourguignon & Hassan S. Bakouch, 2018. "An INAR(1) model with Poisson-Lindley innovations," Economics Bulletin, AccessEcon, vol. 38(3), pages 1505-1513.
    • Handle: RePEc:ebl:ecbull:eb-17-01004
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    File URL: http://www.accessecon.com/Pubs/EB/2018/Volume38/EB-18-V38-I3-P142.pdf
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    References listed on IDEAS

    as
    1. Schweer, Sebastian & Weiß, Christian H., 2014. "Compound Poisson INAR(1) processes: Stochastic properties and testing for overdispersion," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 267-284.
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    Cited by:

    1. Johannes Ferreira & Ané van der Merwe, 2022. "A Noncentral Lindley Construction Illustrated in an INAR(1) Environment," Stats, MDPI, vol. 5(1), pages 1-19, January.
    2. Muhammed Rasheed Irshad & Christophe Chesneau & Veena D’cruz & Naushad Mamode Khan & Radhakumari Maya, 2022. "Bivariate Poisson 2Sum-Lindley Distributions and the Associated BINAR(1) Processes," Mathematics, MDPI, vol. 10(20), pages 1-24, October.
    3. Irshad, M.R. & Jodrá, P. & Krishna, A. & Maya, R., 2023. "On the discrete analogue of the Teissier distribution and its associated INAR(1) process," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 227-245.
    4. R. Maya & Jie Huang & M. R. Irshad & Fukang Zhu, 2024. "On Poisson Moment Exponential Distribution with Associated Regression and INAR(1) Process," Annals of Data Science, Springer, vol. 11(5), pages 1741-1759, October.
    5. Emrah Altun & Naushad Mamode Khan, 2022. "Modelling with the Novel INAR(1)-PTE Process," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1735-1751, September.
    6. Muhammed Rasheed Irshad & Sreedeviamma Aswathy & Radhakumari Maya & Saralees Nadarajah, 2023. "New One-Parameter Over-Dispersed Discrete Distribution and Its Application to the Nonnegative Integer-Valued Autoregressive Model of Order One," Mathematics, MDPI, vol. 12(1), pages 1-14, December.
    7. Ané van der Merwe & Johannes T. Ferreira, 2022. "An Adapted Discrete Lindley Model Emanating from Negative Binomial Mixtures for Autoregressive Counts," Mathematics, MDPI, vol. 10(21), pages 1-21, November.

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    More about this item

    Keywords

    Binomial thinning operator; Estimation; INAR(1) process; Poisson-Lindley distribution;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics

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