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A geometric bivariate time series with different marginal parameters


  • 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

    1. Nadjib Bouzar & K. Jayakumar, 2008. "Time series with discrete semistable marginals," Statistical Papers, Springer, vol. 49(4), pages 619-635, October.
    2. Varadhan, Ravi & Gilbert, Paul, 2009. "BB: An R Package for Solving a Large System of Nonlinear Equations and for Optimizing a High-Dimensional Nonlinear Objective Function," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i04).
    3. 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.
    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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