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Inference for pth‐order random coefficient integer‐valued autoregressive processes

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  • Haitao Zheng
  • Ishwar V. Basawa
  • Somnath Datta

Abstract

. A pth‐order random coefficient integer‐valued autoregressive [RCINAR(p)] model is proposed for count data. Stationarity and ergodicity properties are established. Maximum likelihood, conditional least squares, modified quasi‐likelihood and generalized method of moments are used to estimate the model parameters. Asymptotic properties of the estimators are derived. Simulation results on the comparison of the estimators are reported. The models are applied to two real data sets.

Suggested Citation

  • Haitao Zheng & Ishwar V. Basawa & Somnath Datta, 2006. "Inference for pth‐order random coefficient integer‐valued autoregressive processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(3), pages 411-440, May.
    • Handle: RePEc:bla:jtsera:v:27:y:2006:i:3:p:411-440
    DOI: 10.1111/j.1467-9892.2006.00472.x
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    Cited by:

    1. Shengqi Tian & Dehui Wang & Shuai Cui, 2020. "A seasonal geometric INAR process based on negative binomial thinning operator," Statistical Papers, Springer, vol. 61(6), pages 2561-2581, December.
    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. Aknouche, Abdelhakim & Francq, Christian, 2023. "Two-stage weighted least squares estimator of the conditional mean of observation-driven time series models," Journal of Econometrics, Elsevier, vol. 237(2).
    4. Jiwon Kang & Sangyeol Lee, 2009. "Parameter change test for random coefficient integer‐valued autoregressive processes with application to polio data analysis," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(2), pages 239-258, March.
    5. Xinyang Wang & Dehui Wang & Haixiang Zhang, 2020. "Poisson autoregressive process modeling via the penalized conditional maximum likelihood procedure," Statistical Papers, Springer, vol. 61(1), pages 245-260, February.
    6. Yousung Park & Hee-Young Kim, 2012. "Diagnostic checks for integer-valued autoregressive models using expected residuals," Statistical Papers, Springer, vol. 53(4), pages 951-970, November.
    7. Zheng, Haitao & Basawa, Ishwar V., 2008. "First-order observation-driven integer-valued autoregressive processes," Statistics & Probability Letters, Elsevier, vol. 78(1), pages 1-9, January.
    8. Aknouche, Abdelhakim & Gouveia, Sonia & Scotto, Manuel, 2023. "Random multiplication versus random sum: auto-regressive-like models with integer-valued random inputs," MPRA Paper 119518, University Library of Munich, Germany, revised 18 Dec 2023.
    9. Han Li & Kai Yang & Shishun Zhao & Dehui Wang, 2018. "First-order random coefficients integer-valued threshold autoregressive processes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(3), pages 305-331, July.
    10. Manik Awale & N. Balakrishna & T. V. Ramanathan, 2019. "Testing the constancy of the thinning parameter in a random coefficient integer autoregressive model," Statistical Papers, Springer, vol. 60(5), pages 1515-1539, October.
    11. Nastić, Aleksandar S. & Ristić, Miroslav M., 2012. "Some geometric mixed integer-valued autoregressive (INAR) models," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 805-811.
    12. Doukhan, Paul & Fokianos, Konstantinos & Li, Xiaoyin, 2012. "On weak dependence conditions: The case of discrete valued processes," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1941-1948.
    13. Miroslav M. Ristić & Aleksandar S. Nastić & Ana V. Miletić Ilić, 2013. "A geometric time series model with dependent Bernoulli counting series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 466-476, July.
    14. Chen Xi & Wang Lihong, 2013. "Conditional L1 estimation for random coefficient integer-valued autoregressive processes," Statistics & Risk Modeling, De Gruyter, vol. 30(3), pages 221-235, August.
    15. Aleksandar S. Nastić & Petra N. Laketa & Miroslav M. Ristić, 2016. "Random environment integer-valued autoregressive process," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(2), pages 267-287, March.
    16. repec:tiu:tiutis:6b90fe6f-4de9-4192-9f4d-99ae9220af75 is not listed on IDEAS
    17. 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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