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Parameter Change Test for Poisson Autoregressive Models

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  • Jiwon Kang
  • Sangyeol Lee

Abstract

type="main" xml:id="sjos12088-abs-0001"> In this paper, we consider the problem of testing for a parameter change in Poisson autoregressive models. We suggest two types of cumulative sum (CUSUM) tests, namely, those based on estimates and residuals. We first demonstrate that the conditional maximum likelihood estimator (CMLE) is strongly consistent and asymptotically normal and then construct the CMLE-based CUSUM test. It is shown that under regularity conditions, its limiting null distribution is a function of independent Brownian bridges. Next, we construct the residual-based CUSUM test and derive its limiting null distribution. Simulation results are provided for illustration. A real-data analysis is performed on data for polio incidence and campylobacteriosis infections.

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  • 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.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:4:p:1136-1152
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    References listed on IDEAS

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    15. 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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    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. William Kengne & Isidore S. Ngongo, 2022. "Inference for nonstationary time series of counts with application to change-point problems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 801-835, August.
    3. Cathy W. S. Chen & Sangyeol Lee, 2017. "Bayesian causality test for integer-valued time series models with applications to climate and crime data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(4), pages 797-814, August.
    4. Mamadou Lamine Diop & William Kengne, 2022. "Poisson QMLE for change-point detection in general integer-valued time series models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(3), pages 373-403, April.
    5. 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.
    6. Kang, Jiwon & Song, Junmo, 2017. "Score test for parameter change in Poisson autoregressive models," Economics Letters, Elsevier, vol. 160(C), pages 33-37.
    7. 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.
    8. Haejune Oh & Sangyeol Lee, 2019. "Modified residual CUSUM test for location-scale time series models with heteroscedasticity," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1059-1091, October.
    9. 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.
    10. 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.
    11. Lee, Sangyeol & Kim, Dongwon & Kim, Byungsoo, 2023. "Modeling and inference for multivariate time series of counts based on the INGARCH scheme," Computational Statistics & Data Analysis, Elsevier, vol. 177(C).
    12. Song, Junmo & Kang, Jiwon, 2018. "Parameter change tests for ARMA–GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 41-56.
    13. 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.
    14. Byungsoo Kim & Sangyeol Lee, 2020. "Robust estimation for general integer-valued time series models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(6), pages 1371-1396, December.
    15. Yunwei Cui & Rongning Wu & Qi Zheng, 2021. "Estimation of change‐point for a class of count time series models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1277-1313, December.
    16. Cui, Yunwei & Wu, Rongning, 2016. "On conditional maximum likelihood estimation for INGARCH(p,q) models," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 1-7.
    17. Lee, Sangyeol & Oh, Haejune, 2015. "Entropy test and residual empirical process for autoregressive conditional duration models," Computational Statistics & Data Analysis, Elsevier, vol. 86(C), pages 1-12.
    18. Chigozie E. Utazi, 2017. "Bayesian Single Changepoint Estimation in a Parameter-driven Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(3), pages 765-779, September.
    19. 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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