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A geometric bivariate time series with different marginal parameters

Author

Listed:
  • Predrag M. Popović

    (University of Niš)

  • Miroslav M. Ristić

    (University of Niš)

  • Aleksandar S. Nastić

    (University of Niš)

Abstract

A new bivariate non-negative integer-valued autoregressive model of order one is introduced. The model is based on the binomial thinning operator. The univariate processes that compose the model are geometrically distributed with not necessarily equal mean parameters. Some properties of the model are derived and discussed. The unknown parameters are estimated and some of their asymptotic properties are derived and discussed. The model performance is tested on real data.

Suggested Citation

  • Predrag M. Popović & Miroslav M. Ristić & Aleksandar S. Nastić, 2016. "A geometric bivariate time series with different marginal parameters," Statistical Papers, Springer, vol. 57(3), pages 731-753, September.
    • Handle: RePEc:spr:stpapr:v:57:y:2016:i:3:d:10.1007_s00362-015-0677-z
    DOI: 10.1007/s00362-015-0677-z
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    References listed on IDEAS

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    1. Mátyás Barczy & Márton Ispány & Gyula Pap & Manuel Scotto & Maria Silva, 2012. "Additive outliers in INAR(1) models," Statistical Papers, Springer, vol. 53(4), pages 935-949, November.
    2. Nadjib Bouzar & K. Jayakumar, 2008. "Time series with discrete semistable marginals," Statistical Papers, Springer, vol. 49(4), pages 619-635, October.
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    4. Lee S. Dewald & Peter A. W. Lewis & Ed McKenzie, 1989. "A Bivariate First-Order Autoregressive Time Series Model in Exponential Variables (BEAR(1))," Management Science, INFORMS, vol. 35(10), pages 1236-1246, October.
    5. Robert Jung & Gerd Ronning & A. Tremayne, 2005. "Estimation in conditional first order autoregression with discrete support," Statistical Papers, Springer, vol. 46(2), pages 195-224, April.
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    Cited by:

    1. 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.
    2. Predrag M. Popović & Hassan S. Bakouch, 2020. "A bivariate integer-valued bilinear autoregressive model with random coefficients," Statistical Papers, Springer, vol. 61(5), pages 1819-1840, October.
    3. 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.
    4. Zezhun Chen & Angelos Dassios & George Tzougas, 2023. "Multivariate mixed Poisson Generalized Inverse Gaussian INAR(1) regression," Computational Statistics, Springer, vol. 38(2), pages 955-977, June.
    5. 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.

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