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A new estimation for INAR(1) process with Poisson distribution

Author

Listed:
  • Feilong Lu

    (University of Science and Technology Liaoning
    Jilin University)

  • Dehui Wang

    (Liaoning University)

Abstract

The first-order Poisson autoregressive model may be suitable in situations where the time series data are non-negative integer valued. In this article, we propose a new parameter estimator based on empirical likelihood. Our results show that it can lead to efficient estimators by making effective use of auxiliary information. As a by-product, a test statistic is given, testing the randomness of the parameter. The simulation values show that the proposed test statistic works well. We have applied the suggested method to a real count series.

Suggested Citation

  • Feilong Lu & Dehui Wang, 2022. "A new estimation for INAR(1) process with Poisson distribution," Computational Statistics, Springer, vol. 37(3), pages 1185-1201, July.
    • Handle: RePEc:spr:compst:v:37:y:2022:i:3:d:10.1007_s00180-021-01157-5
    DOI: 10.1007/s00180-021-01157-5
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    References listed on IDEAS

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    1. 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.
    2. Zhiwen Zhao & Wei Yu, 2016. "Empirical Likelihood Inference for First-Order Random Coefficient Integer-Valued Autoregressive Processes," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-8, February.
    3. A. Alzaid & M. Al‐Osh, 1988. "First‐Order Integer‐Valued Autoregressive (INAR (1)) Process: Distributional and Regression Properties," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 42(1), pages 53-61, March.
    4. R. K. Freeland & B. P. M. McCabe, 2004. "Analysis of low count time series data by poisson autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 701-722, September.
    5. 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.
    6. Haixiang Zhang & Dehui Wang & Fukang Zhu, 2011. "Empirical likelihood inference for random coefficient INAR(p) process," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(3), pages 195-203, May.
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