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Bivariate random coefficient integer‐valued autoregressive models: Parameter estimation and change point test

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  • Sangyeol Lee
  • Minyoung Jo

Abstract

This study examines a first‐order bivariate random coefficient integer‐valued autoregressive (BRCINAR) model and the inferential procedures of this model, such as the parameter estimation and parameter change test. We first introduce the BRCINAR model and investigate its probabilistic properties such as stationarity, ergodicity, and high moment conditions, and then propose estimation methods such as the conditional least squares (CLS), modified quasi‐likelihood (MQL), and exponential family quasi‐likelihood (EQL) methods. As an application, a parameter change test is considered. For this task, a residual‐based cumulative sum (CUSUM) test is employed. To evaluate the performances of the three estimation methods and the respective CUSUM tests, we conduct a Monte Carlo simulation study and demonstrate the adequacy of the proposed methods. A real data analysis is also carried out using syphilis data in the United States for illustration.

Suggested Citation

  • Sangyeol Lee & Minyoung Jo, 2023. "Bivariate random coefficient integer‐valued autoregressive models: Parameter estimation and change point test," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(5-6), pages 644-666, September.
    • Handle: RePEc:bla:jtsera:v:44:y:2023:i:5-6:p:644-666
    DOI: 10.1111/jtsa.12662
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    References listed on IDEAS

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    1. Fokianos, Konstantinos & Rahbek, Anders & Tjøstheim, Dag, 2009. "Poisson Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1430-1439.
    2. Ali Ahmad & Christian Francq, 2016. "Poisson QMLE of Count Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(3), pages 291-314, May.
    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. 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.
    5. Serge Darolles & Gaëlle Le Fol & Yang Lu & Ran Sun, 2018. "Bivariate integer-autoregressive process with an application to mutual fund flows," Post-Print hal-04590149, HAL.
    6. 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.
    7. 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.
    8. Byungsoo Kim & Sangyeol Lee, 2013. "Robust estimation for copula Parameter in SCOMDY models," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(3), pages 302-314, May.
    9. Jürgen Franke & Claudia Kirch & Joseph Tadjuidje Kamgaing, 2012. "Changepoints in times series of counts," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(5), pages 757-770, September.
    10. Darolles, Serge & Fol, Gaëlle Le & Lu, Yang & Sun, Ran, 2019. "Bivariate integer-autoregressive process with an application to mutual fund flows," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 181-203.
    11. 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.
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