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Parameter change test for random coefficient integer‐valued autoregressive processes with application to polio data analysis

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  • Jiwon Kang
  • Sangyeol Lee

Abstract

. In this paper, we consider the problem of testing for a parameter change in a first‐order random coefficient integer‐valued autoregressive [RCINAR(1)] model. We employ the cumulative sum (CUSUM) test based on the conditional least‐squares and modified quasi‐likelihood estimators. It is shown that under regularity conditions, the CUSUM test has the same limiting distribution as the supremum of the squares of independent Brownian bridges. The CUSUM test is then applied to the analysis of the monthly polio counts data set.

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  • 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.
    • Handle: RePEc:bla:jtsera:v:30:y:2009:i:2:p:239-258
    DOI: 10.1111/j.1467-9892.2009.00608.x
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    References listed on IDEAS

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    1. Lee, Sangyeol & Na, Okyoung, 2005. "Test for parameter change in stochastic processes based on conditional least-squares estimator," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 375-393, April.
    2. Sangyeol Lee & Jeongcheol Ha & Okyoung Na & Seongryong Na, 2003. "The Cusum Test for Parameter Change in Time Series Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(4), pages 781-796, December.
    3. 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.
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    Cited by:

    1. Kang, Jiwon & Song, Junmo, 2015. "Robust parameter change test for Poisson autoregressive models," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 14-21.
    2. Mamadou Lamine Diop & William Kengne, 2017. "Testing Parameter Change in General Integer-Valued Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 880-894, November.
    3. Šárka Hudecová & Marie Hušková & Simos G. Meintanis, 2017. "Tests for Structural Changes in Time Series of Counts," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 843-865, December.
    4. Kang, Jiwon & Song, Junmo, 2017. "Score test for parameter change in Poisson autoregressive models," Economics Letters, Elsevier, vol. 160(C), pages 33-37.
    5. Mamadou Lamine Diop & William Kengne, 2023. "A general procedure for change-point detection in multivariate time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 1-33, March.
    6. Jiwon Kang & Sangyeol Lee, 2014. "Parameter Change Test for Poisson Autoregressive Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1136-1152, December.
    7. 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.
    8. Youngmi Lee & Sangyeol Lee & Dag Tjøstheim, 2018. "Asymptotic normality and parameter change test for bivariate Poisson INGARCH models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 52-69, March.
    9. Kang, Jiwon & Lee, Sangyeol, 2014. "Minimum density power divergence estimator for Poisson autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 44-56.
    10. 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.
    11. Youngmi Lee & Sangyeol Lee, 2019. "CUSUM test for general nonlinear integer-valued GARCH models: comparison study," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1033-1057, October.

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