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A model for integer-valued time series with conditional overdispersion

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  • Xu, Hai-Yan
  • Xie, Min
  • Goh, Thong Ngee
  • Fu, Xiuju

Abstract

In this paper, a new model, motivated by the weekly dengue cases in Singapore from year 2001 to 2010, is proposed to handle the conditional equidispersion, overdispersion and underdispersion in integer-valued pure time series. It is shown that the INARCH model studied by earlier researchers is a special case. Conditions for weak and strict stationarity of this model are also given in our paper. Some basic properties of this model are shown to be parallel to those of the classical autoregressive model. Three distribution based methods and two non-distribution based methods are presented for parameter estimation. These methods are compared in a simulation study for the conditional overdispersed situation with an integer-valued pure time series of order one. Finally, this model is applied to the motivating example.

Suggested Citation

  • Xu, Hai-Yan & Xie, Min & Goh, Thong Ngee & Fu, Xiuju, 2012. "A model for integer-valued time series with conditional overdispersion," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4229-4242.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:12:p:4229-4242
    DOI: 10.1016/j.csda.2012.04.011
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    2. Christian H. Weiß & Esmeralda Gonçalves & Nazaré Mendes Lopes, 2017. "Testing the compounding structure of the CP-INARCH model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(5), pages 571-603, July.
    3. Chen, Cathy W.S. & Chen, Chun-Shu & Hsiung, Mo-Hua, 2023. "Bayesian modeling of spatial integer-valued time series," Computational Statistics & Data Analysis, Elsevier, vol. 188(C).
    4. Vladim'ir Hol'y & Petra Tomanov'a, 2021. "Modeling Price Clustering in High-Frequency Prices," Papers 2102.12112, arXiv.org, revised Mar 2021.
    5. Yang Lu, 2021. "The predictive distributions of thinning‐based count processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 42-67, March.
    6. Pedeli, Xanthi & Karlis, Dimitris, 2013. "Some properties of multivariate INAR(1) processes," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 213-225.
    7. Sebastian Schweer, 2016. "A Goodness-of-Fit Test for Integer-Valued Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 77-98, January.
    8. Huiyu Mao & Fukang Zhu & Yan Cui, 2020. "A generalized mixture integer-valued GARCH model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(3), pages 527-552, September.
    9. Christian H. Weiß & Sebastian Schweer, 2015. "Detecting overdispersion in INARCH(1) processes," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(3), pages 281-297, August.
    10. Sáez-Castillo, A.J. & Conde-Sánchez, A., 2013. "A hyper-Poisson regression model for overdispersed and underdispersed count data," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 148-157.
    11. E. Gonçalves & N. Mendes-Lopes & F. Silva, 2015. "Infinitely Divisible Distributions in Integer-Valued Garch Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(4), pages 503-527, July.

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