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INAR(1) Processes with Inflated-parameter Generalized Power Series Innovations

Author

Listed:
  • Lívio Tito

    (Departamento de Estatística, Universidade Federal do Rio Grande do Norte, Lagoa Nova, Natal, RN, Brazil)

  • Bourguignon Marcelo

    (Departamento de Estatística, Universidade Federal do Rio Grande do Norte, Lagoa Nova, Natal, RN, Brazil)

  • Nascimento Fernando

    (Departamento de Estatística, Universidade Federal do Piauí, Teresina, PI, Brazil)

Abstract

In this paper, new models are studied by proposing the family of generalized power series distributions with inflated parameter (IGPSD) for the innovation process of the INAR(1) model. The main properties of the process were established, such as mean, variance, autocorrelation and transition probability. The methods of estimation by Yule–Walker and the conditional maximum likelihood were used to estimate the parameters of the models. Two particular cases of the INAR(1)$\left(1\right)$ model with IGPSD innovation were studied, named IPoINAR(1)$\left(1\right)$ and IGeoINAR(1)$\left(1\right)$. Finally, in the real data example, a good performance of the proposed new models was observed.

Suggested Citation

  • Lívio Tito & Bourguignon Marcelo & Nascimento Fernando, 2020. "INAR(1) Processes with Inflated-parameter Generalized Power Series Innovations," Journal of Time Series Econometrics, De Gruyter, vol. 12(2), pages 1-27, July.
    • Handle: RePEc:bpj:jtsmet:v:12:y:2020:i:2:p:27:n:2
    DOI: 10.1515/jtse-2019-0033
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    References listed on IDEAS

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