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

  • Christian Weiß

    ()

  • Hee-Young Kim

    ()

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    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

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    File URL: http://hdl.handle.net/10.1007/s00362-012-0449-y
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    Article provided by Springer in its journal Statistical Papers.

    Volume (Year): 54 (2013)
    Issue (Month): 3 (August)
    Pages: 563-590

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    Handle: RePEc:spr:stpapr:v:54:y:2013:i:3:p:563-590
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    1. Brännäs, Kurt & Quoreshi, Shahiduzzaman, 2004. "Integer-Valued Moving Average Modelling of the Number of Transactions in Stocks," Umeå Economic Studies 637, Umeå University, Department of Economics.
    2. Konstantinos Fokianos & Anders Rahbek & Dag Tjøstheim, 2008. "Poisson Autoregression," Discussion Papers 08-35, University of Copenhagen. Department of Economics, revised Dec 2008.
    3. 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.
    4. 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.
    5. Heinen, Andreas, 2003. "Modelling Time Series Count Data: An Autoregressive Conditional Poisson Model," MPRA Paper 8113, University Library of Munich, Germany.
    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. Robert Jung & A. Tremayne, 2011. "Useful models for time series of counts or simply wrong ones?," AStA Advances in Statistical Analysis, Springer, vol. 95(1), pages 59-91, March.
    8. Marcus J Chambers, 2010. "Jackknife Estimation of Stationary Autoregressive Models," Economics Discussion Papers 684, University of Essex, Department of Economics.
    9. Christian Weiß, 2008. "Thinning operations for modeling time series of counts—a survey," AStA Advances in Statistical Analysis, Springer, vol. 92(3), pages 319-341, August.
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