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On the theory of periodic multivariate INAR processes

Author

Listed:
  • Cláudia Santos

    (University of Aveiro
    Polytechnic Institute of Coimbra)

  • Isabel Pereira

    (University of Aveiro)

  • Manuel G. Scotto

    (IST University of Lisbon)

Abstract

In this paper a multivariate integer-valued autoregressive model of order one with periodic time-varying parameters, and driven by a periodic innovations sequence of independent random vectors is introduced and studied in detail. Emphasis is placed on models with periodic multivariate negative binomial innovations. Basic probabilistic and statistical properties of the novel model are discussed. Aiming to reduce computational burden arising from the use of the conditional maximum likelihood method, a composite likelihood-based approach is adopted. The performance of such method is compared with that of some traditional competitors, namely moment estimators and conditional maximum likelihood estimators. Forecasting is also addressed. Furthermore, an application to a real data set concerning the monthly number of fires in three counties in Portugal is presented.

Suggested Citation

  • Cláudia Santos & Isabel Pereira & Manuel G. Scotto, 2021. "On the theory of periodic multivariate INAR processes," Statistical Papers, Springer, vol. 62(3), pages 1291-1348, June.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:3:d:10.1007_s00362-019-01136-5
    DOI: 10.1007/s00362-019-01136-5
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    References listed on IDEAS

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    1. Hee-Young Kim & Yousung Park, 2008. "A non-stationary integer-valued autoregressive model," Statistical Papers, Springer, vol. 49(3), pages 485-502, July.
    2. Cristiano Varin, 2008. "On composite marginal likelihoods," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(1), pages 1-28, February.
    3. Cristiano Varin & Paolo Vidoni, 2005. "A note on composite likelihood inference and model selection," Biometrika, Biometrika Trust, vol. 92(3), pages 519-528, September.
    4. Joe, Harry & Lee, Youngjo, 2009. "On weighting of bivariate margins in pairwise likelihood," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 670-685, April.
    5. Yuvraj Sunecher & Naushad Mamode Khan & Miroslav M. Ristić & Vandna Jowaheer, 2019. "BINAR(1) negative binomial model for bivariate non-stationary time series with different over-dispersion indices," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(4), pages 625-653, December.
    6. N. Mamode Khan & Y. Sunecher & V. Jowaheer & M. M. Ristic & M. Heenaye-Mamode Khan, 2019. "Investigating GQL-based inferential approaches for non-stationary BINAR(1) model under different quantum of over-dispersion with application," Computational Statistics, Springer, vol. 34(3), pages 1275-1313, September.
    7. Miroslav M. Ristić & Yuvraj Sunecher & Naushad Mamode Khan & Vandna Jowaheer, 2019. "A GQL-based inference in non-stationary BINMA(1) time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 969-998, September.
    8. Tobias A. Möller & Maria Eduarda Silva & Christian H. Weiß & Manuel G. Scotto & Isabel Pereira, 2016. "Self-exciting threshold binomial autoregressive processes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(4), pages 369-400, October.
    9. Quoreshi, A.M.M. Shahiduzzaman, 2008. "A vector integer-valued moving average model for high frequency financial count data," Economics Letters, Elsevier, vol. 101(3), pages 258-261, December.
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    11. Marj Tonini & Mário Gonzalez Pereira & Joana Parente & Carmen Vega Orozco, 2017. "Evolution of forest fires in Portugal: from spatio-temporal point events to smoothed density maps," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 85(3), pages 1489-1510, February.
    12. Jan Bulla & Christophe Chesneau & Maher Kachour, 2017. "A bivariate first-order signed integer-valued autoregressive process," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(13), pages 6590-6604, July.
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    Cited by:

    1. Jiajie Kong & Robert Lund, 2023. "Seasonal count time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(1), pages 93-124, January.

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