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Bivariate binomial autoregressive models

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  • Scotto, Manuel G.
  • Weiß, Christian H.
  • Silva, Maria Eduarda
  • Pereira, Isabel

Abstract

This paper introduces new classes of bivariate time series models being useful to fit count data time series with a finite range of counts. Motivation comes mainly from the comparison of schemes for monitoring tourism demand, stock data, production and environmental processes. All models are based on the bivariate binomial distribution of Type II. First, a new family of bivariate integer-valued GARCH models is proposed. Then, a new bivariate thinning operation is introduced and explained in detail. The new thinning operation has a number of advantages including the fact that marginally it behaves as the usual binomial thinning operation and also that allows for both positive and negative cross-correlations. Based upon this new thinning operation, a bivariate extension of the binomial autoregressive model of order one is introduced. Basic probabilistic and statistical properties of the model are discussed. Parameter estimation and forecasting are also covered. The performance of these models is illustrated through an empirical application to a set of rainy days time series collected from 2000 up to 2010 in the German cities of Bremen and Cuxhaven.

Suggested Citation

  • Scotto, Manuel G. & Weiß, Christian H. & Silva, Maria Eduarda & Pereira, Isabel, 2014. "Bivariate binomial autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 233-251.
    • Handle: RePEc:eee:jmvana:v:125:y:2014:i:c:p:233-251
    DOI: 10.1016/j.jmva.2013.12.014
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    2. Zhang, Rui, 2024. "Asymmetric beta-binomial GARCH models for time series with bounded support," Applied Mathematics and Computation, Elsevier, vol. 470(C).
    3. Fokianos, Konstantinos, 2024. "Multivariate Count Time Series Modelling," Econometrics and Statistics, Elsevier, vol. 31(C), pages 100-116.
    4. Serge Darolles & Gaëlle Le Fol & Yang Lu & Ran Sun, 2018. "Bivariate integer-autoregressive process with an application to mutual fund flows," Post-Print hal-04590149, HAL.
    5. Qingchun Zhang & Dehui Wang & Xiaodong Fan, 2020. "A negative binomial thinning‐based bivariate INAR(1) process," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(4), pages 517-537, November.
    6. 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.
    7. Huaping Chen & Fukang Zhu & Xiufang Liu, 2022. "A New Bivariate INAR(1) Model with Time-Dependent Innovation Vectors," Stats, MDPI, vol. 5(3), pages 1-22, August.
    8. Yao Kang & Dehui Wang & Kai Yang, 2021. "A new INAR(1) process with bounded support for counts showing equidispersion, underdispersion and overdispersion," Statistical Papers, Springer, vol. 62(2), pages 745-767, April.
    9. Yao Kang & Shuhui Wang & Dehui Wang & Fukang Zhu, 2023. "Analysis of zero-and-one inflated bounded count time series with applications to climate and crime data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 34-73, March.
    10. Han Li & Zijian Liu & Kai Yang & Xiaogang Dong & Wenshan Wang, 2024. "A pth-order random coefficients mixed binomial autoregressive process with explanatory variables," Computational Statistics, Springer, vol. 39(5), pages 2581-2604, July.
    11. 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).
    12. Darolles, Serge & Fol, Gaëlle Le & Lu, Yang & Sun, Ran, 2019. "Bivariate integer-autoregressive process with an application to mutual fund flows," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 181-203.
    13. Kai Yang & Yiwei Zhao & Han Li & Dehui Wang, 2023. "On bivariate threshold Poisson integer-valued autoregressive processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(8), pages 931-963, November.
    14. Luiza S. C. Piancastelli & Wagner Barreto‐Souza & Hernando Ombao, 2023. "Flexible bivariate INGARCH process with a broad range of contemporaneous correlation," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(2), pages 206-222, March.

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