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A Poisson INAR(1) model with serially dependent innovations

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  • Christian Weiß

Abstract

Motivated by a certain type of infinite-patch metapopulation model, we propose an extension to the popular Poisson INAR(1) model, where the innovations are assumed to be serially dependent in such a way that their mean is increased if the current population is large. We shall recognize that this new model forms a bridge between the Poisson INAR(1) model and the INARCH(1) model. We analyze the stochastic properties of the observations and innovations from an extended Poisson INAR(1) process, and we consider the problem of model identification and parameter estimation. A real-data example about iceberg counts shows how to benefit from the new model. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Christian Weiß, 2015. "A Poisson INAR(1) model with serially dependent innovations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(7), pages 829-851, October.
    • Handle: RePEc:spr:metrik:v:78:y:2015:i:7:p:829-851
    DOI: 10.1007/s00184-015-0529-9
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    References listed on IDEAS

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    1. Frey, Stefan & Sandås, Patrik, 2009. "The impact of iceberg orders in limit order books," CFR Working Papers 09-06, University of Cologne, Centre for Financial Research (CFR).
    2. R. K. Freeland & B. P. M. McCabe, 2004. "Analysis of low count time series data by poisson autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 701-722, September.
    3. Robert C. Jung & A. R. Tremayne, 2003. "Testing for serial dependence in time series models of counts," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(1), pages 65-84, January.
    4. Christian Weiß, 2008. "Thinning operations for modeling time series of counts—a survey," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(3), pages 319-341, August.
    5. Jiajing Sun & Brendan P. McCabe, 2013. "Score statistics for testing serial dependence in count data," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(3), pages 315-329, May.
    6. Christian H. Weiß & Philip K. Pollett, 2014. "Binomial Autoregressive Processes With Density-Dependent Thinning," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(2), pages 115-132, March.
    7. Ruijun Bu & Brendan McCabe & Kaddour Hadri, 2008. "Maximum likelihood estimation of higher‐order integer‐valued autoregressive processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(6), pages 973-994, November.
    8. Ruey S. Tsay, 1992. "Model Checking Via Parametric Bootstraps in Time Series Analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(1), pages 1-15, March.
    9. Fukang Zhu & Dehui Wang, 2011. "Estimation and testing for a Poisson autoregressive model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(2), pages 211-230, March.
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