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Parameter estimation for binomial AR(1) models with applications in finance and industry


  • Christian Weiß


  • Hee-Young Kim



Methods for analyzing and modeling count data time series are used in various fields of practice, and they are particularly relevant for applications in finance and economy. We consider the binomial autoregressive (AR(1)) model for count data processes with a first-order AR dependence structure and a binomial marginal distribution. We present four approaches for estimating its model parameters based on given time series data, and we derive expressions for the asymptotic distribution of these estimators. Then we investigate the finite-sample performance of the estimators and of the respective asymptotic approximations in a simulation study, including a discussion of the 2-block jackknife. We illustrate our methods and findings with a real-data example about transactions at the Korea stock market. We conclude with an application of our results for obtaining reliable estimates for process capability indices. Copyright Springer-Verlag 2013

Suggested Citation

  • Christian Weiß & Hee-Young Kim, 2013. "Parameter estimation for binomial AR(1) models with applications in finance and industry," Statistical Papers, Springer, vol. 54(3), pages 563-590, August.
  • Handle: RePEc:spr:stpapr:v:54:y:2013:i:3:p:563-590 DOI: 10.1007/s00362-012-0449-y

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    References listed on IDEAS

    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. 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. Chambers, Marcus J., 2013. "Jackknife estimation of stationary autoregressive models," Journal of Econometrics, Elsevier, vol. 172(1), pages 142-157.
    6. Peter C. B. Phillips, 2005. "Jackknifing Bond Option Prices," Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 707-742.
    7. Heinen, Andreas, 2003. "Modelling Time Series Count Data: An Autoregressive Conditional Poisson Model," MPRA Paper 8113, University Library of Munich, Germany.
    8. Jung, Robert C. & Kukuk, Martin & Liesenfeld, Roman, 2006. "Time series of count data: modeling, estimation and diagnostics," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2350-2364, December.
    9. 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. 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.
    2. Weiß, Christian H. & Schweer, Sebastian, 2016. "Bias corrections for moment estimators in Poisson INAR(1) and INARCH(1) processes," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 124-130.


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