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Compound Poisson INAR(1) processes: Stochastic properties and testing for overdispersion

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  • Schweer, Sebastian
  • Weiß, Christian H.

Abstract

The compound Poisson INAR(1) model for time series of overdispersed counts is considered. For such CPINAR(1) processes, explicit results are derived for joint moments, for the k-step-ahead distribution as well as for the stationary distribution. It is shown that a CPINAR(1) process is strongly mixing with exponentially decreasing weights. This result is utilized to design a test for overdispersion in INAR(1) processes and to derive its asymptotic power function. An application of our results to a real-data example and a study of the finite-sample performance of the test are presented.

Suggested Citation

  • Schweer, Sebastian & Weiß, Christian H., 2014. "Compound Poisson INAR(1) processes: Stochastic properties and testing for overdispersion," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 267-284.
  • Handle: RePEc:eee:csdana:v:77:y:2014:i:c:p:267-284
    DOI: 10.1016/j.csda.2014.03.005
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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. repec:spr:stpapr:v:58:y:2017:i:2:d:10.1007_s00362-015-0704-0 is not listed on IDEAS
    2. Raju Maiti & Atanu Biswas & Samarjit Das, 2016. "Coherent forecasting for count time series using Box–Jenkins's AR(p) model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(2), pages 123-145, May.
    3. repec:spr:testjl:v:26:y:2017:i:4:d:10.1007_s11749-017-0536-4 is not listed on IDEAS
    4. Sebastian Schweer, 2016. "A Goodness-of-Fit Test for Integer-Valued Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 77-98, January.
    5. Marcelo Bourguignon, 2016. "Poisson–geometric INAR(1) process for modeling count time series with overdispersion," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(3), pages 176-192, August.
    6. 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.
    7. Borges, Patrick & Molinares, Fabio Fajardo & Bourguignon, Marcelo, 2016. "A geometric time series model with inflated-parameter Bernoulli counting series," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 264-272.
    8. repec:bla:scjsta:v:44:y:2017:i:4:p:843-865 is not listed on IDEAS
    9. Sebastian Schweer & Christian H. Weiß, 2016. "Testing for Poisson arrivals in INAR(1) processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 503-524, September.
    10. Christian H. Weiß & Sebastian Schweer, 2015. "Detecting overdispersion in INARCH(1) processes," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(3), pages 281-297, August.
    11. Bisaglia, Luisa & Canale, Antonio, 2016. "Bayesian nonparametric forecasting for INAR models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 70-78.
    12. repec:spr:empeco:v:53:y:2017:i:2:d:10.1007_s00181-016-1140-2 is not listed on IDEAS
    13. Wagner Barreto-Souza, 2015. "Zero-Modified Geometric INAR(1) Process for Modelling Count Time Series with Deflation or Inflation of Zeros," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(6), pages 839-852, November.

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