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Bivariate binomial autoregressive models

Listed author(s):
  • Scotto, Manuel G.
  • Weiß, Christian H.
  • Silva, Maria Eduarda
  • Pereira, Isabel
Registered author(s):

    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.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X14000086
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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 125 (2014)
    Issue (Month): C ()
    Pages: 233-251

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    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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    1. Fokianos, Konstantinos & Rahbek, Anders & Tjøstheim, Dag, 2009. "Poisson Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1430-1439.
    2. Kurt Brannas & A. M. M. Shahiduzzaman Quoreshi, 2010. "Integer-valued moving average modelling of the number of transactions in stocks," Applied Financial Economics, Taylor & Francis Journals, vol. 20(18), pages 1429-1440.
    3. Robert Jung & A. Tremayne, 2011. "Useful models for time series of counts or simply wrong ones?," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(1), pages 59-91, March.
    4. Freeland, R. K. & McCabe, B. P. M., 2004. "Forecasting discrete valued low count time series," International Journal of Forecasting, Elsevier, vol. 20(3), pages 427-434.
    5. Jonas Andersson & Dimitris Karlis, 2010. "Treating missing values in INAR(1) models: An application to syndromic surveillance data," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(1), pages 12-19, January.
    6. Yunwei Cui & Robert Lund, 2009. "A new look at time series of counts," Biometrika, Biometrika Trust, vol. 96(4), pages 781-792.
    7. Zhu, Fukang & Wang, Dehui, 2010. "Diagnostic checking integer-valued ARCH(p) models using conditional residual autocorrelations," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 496-508, February.
    8. Zhou, J. & Basawa, I.V., 2005. "Least-squares estimation for bifurcating autoregressive processes," Statistics & Probability Letters, Elsevier, vol. 74(1), pages 77-88, August.
    9. René Ferland & Alain Latour & Driss Oraichi, 2006. "Integer-Valued GARCH Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(6), pages 923-942, November.
    10. Biswas, Atanu & Hwang, Jing-Shiang, 2002. "A new bivariate binomial distribution," Statistics & Probability Letters, Elsevier, vol. 60(2), pages 231-240, November.
    11. Christian H. Weiß & Philip K. Pollett, 2012. "Chain Binomial Models and Binomial Autoregressive Processes," Biometrics, The International Biometric Society, vol. 68(3), pages 815-824, September.
    12. Quoreshi, Shahiduzzaman, 2005. "Bivariate Time Series Modelling of Financial Count Data," Umeå Economic Studies 655, Umeå University, Department of Economics.
    13. Dag Tjøstheim, 2012. "Some recent theory for autoregressive count time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 413-438, September.
    14. Christian Weiß, 2009. "Modelling time series of counts with overdispersion," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 18(4), pages 507-519, November.
    15. Alexandra M. Schmidt & João Batista M. Pereira, 2011. "Modelling Time Series of Counts in Epidemiology," International Statistical Review, International Statistical Institute, vol. 79(1), pages 48-69, April.
    16. Heinen, Andreas & Rengifo, Erick, 2007. "Multivariate autoregressive modeling of time series count data using copulas," Journal of Empirical Finance, Elsevier, vol. 14(4), pages 564-583, September.
    17. Konstantinos Fokianos & Dag Tjøstheim, 2012. "Nonlinear Poisson autoregression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(6), pages 1205-1225, December.
    18. Christian Weiss, 2009. "Monitoring correlated processes with binomial marginals," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(4), pages 399-414.
    19. 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.
    20. Xanthi Pedeli & Dimitris Karlis, 2013. "On composite likelihood estimation of a multivariate INAR(1) model," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(2), pages 206-220, March.
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