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Testing for Poisson arrivals in INAR(1) processes

Author

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  • Sebastian Schweer

    (University of Heidelberg)

  • Christian H. Weiß

    (Helmut Schmidt University)

Abstract

In the framework of integer-valued autoregressive processes of order 1 [INAR(1)], two new tests for the null hypothesis of Poisson-distributed innovations are developed. The tests focus on time reversibility, as this feature is shown to be satisfied exclusively by Poisson INAR(1) processes. The necessary asymptotic variances are explicitly calculated using the joint cumulants of these processes. The finite-sample behavior of the test statistics and the power of the tests are investigated in a simulation study. The results show that the newly developed tests perform better than existing ones in certain situations.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:25:y:2016:i:3:d:10.1007_s11749-015-0466-y
    DOI: 10.1007/s11749-015-0466-y
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    References listed on IDEAS

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    1. René Ferland & Alain Latour & Driss Oraichi, 2006. "Integer‐Valued GARCH Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(6), pages 923-942, November.
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    5. 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.
    6. Simos Meintanis & Dimitris Karlis, 2014. "Validation tests for the innovation distribution in INAR time series models," Computational Statistics, Springer, vol. 29(5), pages 1221-1241, October.
    7. Zacharias Psaradakis, 2008. "Assessing Time‐Reversibility Under Minimal Assumptions," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 881-905, September.
    8. 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.
    9. Puig, Pedro & Valero, Jordi, 2006. "Count Data Distributions: Some Characterizations With Applications," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 332-340, March.
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    Cited by:

    1. Zeng, Xiaoqiang & Kakizawa, Yoshihide, 2024. "Two-step conditional least squares estimation in ADCINAR(1) process, revisited," Statistics & Probability Letters, Elsevier, vol. 206(C).
    2. Boris Aleksandrov & Christian H. Weiß & Carsten Jentsch, 2022. "Goodness‐of‐fit tests for Poisson count time series based on the Stein–Chen identity," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(1), pages 35-64, February.
    3. Boris Aleksandrov & Christian H. Weiß & Simon Nik & Maxime Faymonville & Carsten Jentsch, 2024. "Modelling and diagnostic tests for Poisson and negative-binomial count time series," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(7), pages 843-887, October.
    4. Masoomeh Forughi & Zohreh Shishebor & Atefeh Zamani, 2022. "Portmanteau tests for generalized integer-valued autoregressive time series models," Statistical Papers, Springer, vol. 63(4), pages 1163-1185, August.
    5. Zeng, Xiaoqiang & Kakizawa, Yoshihide, 2022. "Bias-correction of some estimators in the INAR(1) process," Statistics & Probability Letters, Elsevier, vol. 187(C).

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