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Two-step conditional least squares estimation in ADCINAR(1) process, revisited

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  • Zeng, Xiaoqiang
  • Kakizawa, Yoshihide

Abstract

Asymptotic normality of two-step conditional least squares estimator is revisited for the stationary ADCINAR(1) process. It turns out that plugging a consistent estimator for the parameter α affects the resulting asymptotic variance, whereas plugging the sample mean and variance has no effect. The phenomenon cannot be grasped from two examples discussed in Karlsen and Tjøstheim (1988).

Suggested Citation

  • Zeng, Xiaoqiang & Kakizawa, Yoshihide, 2024. "Two-step conditional least squares estimation in ADCINAR(1) process, revisited," Statistics & Probability Letters, Elsevier, vol. 206(C).
    • Handle: RePEc:eee:stapro:v:206:y:2024:i:c:s0167715223002274
    DOI: 10.1016/j.spl.2023.110003
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    References listed on IDEAS

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    1. 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.
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    4. Zeng, Xiaoqiang & Kakizawa, Yoshihide, 2022. "Bias-correction of some estimators in the INAR(1) process," Statistics & Probability Letters, Elsevier, vol. 187(C).
    5. 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.
    6. Aleksandar S. Nastić & Miroslav M. Ristić & Ana V. Miletić Ilić, 2017. "A geometric time-series model with an alternative dependent Bernoulli counting series," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(2), pages 770-785, January.
    7. 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.
    8. 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.
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