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Bias-correction of some estimators in the INAR(1) process

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  • Zeng, Xiaoqiang
  • Kakizawa, Yoshihide

Abstract

A class of estimators in the first-order nonnegative integer-valued autoregressive process is considered, which contains the Yule–Walker, Burg, and method of moment estimators. Bias-correction and higher-order mean squared error comparison are studied. Some simulations demonstrate that the bias-correction works well.

Suggested Citation

  • Zeng, Xiaoqiang & Kakizawa, Yoshihide, 2022. "Bias-correction of some estimators in the INAR(1) process," Statistics & Probability Letters, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:stapro:v:187:y:2022:i:c:s0167715222000839
    DOI: 10.1016/j.spl.2022.109503
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    References listed on IDEAS

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    1. Keith Freeland, R. & McCabe, Brendan, 2005. "Asymptotic properties of CLS estimators in the Poisson AR(1) model," Statistics & Probability Letters, Elsevier, vol. 73(2), pages 147-153, June.
    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. M. A. Al‐Osh & A. A. Alzaid, 1987. "First‐Order Integer‐Valued Autoregressive (Inar(1)) Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(3), pages 261-275, May.
    4. 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.
    5. Yoshihide Kakizawa, 1996. "Third‐Order Asymptotic Properties Of Estimators In Gaussian Arma Processes With Unknown Mean," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(4), pages 367-377, July.
    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. Feike C. Drost & Ramon van den Akker & Bas J. M. Werker, 2009. "Efficient estimation of auto‐regression parameters and innovation distributions for semiparametric integer‐valued AR(p) models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 467-485, April.
    8. 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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