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Non-linear INAR(1) processes under an alternative geometric thinning operator

Author

Listed:
  • Wagner Barreto-Souza

    (University College Dublin
    King Abdullah University of Science and Technology)

  • Sokol Ndreca

    (Universidade Federal de Minas Gerais)

  • Rodrigo B. Silva

    (Universidade Federal da Paraíba)

  • Roger W. C. Silva

    (Universidade Federal de Minas Gerais)

Abstract

We propose a novel class of first-order integer-valued AutoRegressive (INAR(1)) models based on a new operator, the so-called geometric thinning operator, which induces a certain non-linearity to the models. We show that this non-linearity can produce better results in terms of prediction when compared to the linear case commonly considered in the literature. The new models are named non-linear INAR(1) (in short NonLINAR(1)) processes. We explore both stationary and non-stationary versions of the NonLINAR processes. Inference on the model parameters is addressed and the finite-sample behavior of the estimators investigated through Monte Carlo simulations. Two real data sets are analyzed to illustrate the stationary and non-stationary cases and the gain of the non-linearity induced for our method over the existing linear methods. A generalization of the geometric thinning operator and an associated NonLINAR process are also proposed and motivated for dealing with zero-inflated or zero-deflated count time series data.

Suggested Citation

  • Wagner Barreto-Souza & Sokol Ndreca & Rodrigo B. Silva & Roger W. C. Silva, 2023. "Non-linear INAR(1) processes under an alternative geometric thinning operator," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 695-725, June.
    • Handle: RePEc:spr:testjl:v:32:y:2023:i:2:d:10.1007_s11749-023-00849-y
    DOI: 10.1007/s11749-023-00849-y
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    References listed on IDEAS

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    1. Keith Freeland, R. & McCabe, Brendan, 2005. "Asymptotic properties of CLS estimators in the Poisson AR(1) model," Statistics & Probability Letters, Elsevier, vol. 73(2), pages 147-153, June.
    2. Maia, Gisele de Oliveira & Barreto-Souza, Wagner & Bastos, Fernando de Souza & Ombao, Hernando, 2021. "Semiparametric time series models driven by latent factor," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1463-1479.
    3. Rahimov, I., 2008. "Asymptotic distribution of the CLSE in a critical process with immigration," Stochastic Processes and their Applications, Elsevier, vol. 118(10), pages 1892-1908, October.
    4. Littlejohn, R. P., 1996. "A reversibility relationship for two Markovian time series models with stationary geometric tailed distribution," Stochastic Processes and their Applications, Elsevier, vol. 64(1), pages 127-133, November.
    5. Rodrigo B. Silva & Wagner Barreto‐Souza, 2019. "Flexible and Robust Mixed Poisson INGARCH Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 40(5), pages 788-814, September.
    6. Fukang Zhu, 2011. "A negative binomial integer‐valued GARCH model," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(1), pages 54-67, January.
    7. M. A. Al‐Osh & A. A. Alzaid, 1987. "First‐Order Integer‐Valued Autoregressive (Inar(1)) Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(3), pages 261-275, May.
    8. Wagner Barreto-Souza, 2015. "Zero-Modified Geometric INAR(1) Process for Modelling Count Time Series with Deflation or Inflation of Zeros," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(6), pages 839-852, November.
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