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CUSUM test for general nonlinear integer-valued GARCH models: comparison study

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  • Youngmi Lee

    (Seoul National University)

  • Sangyeol Lee

    (Seoul National University)

Abstract

This study considers the problem of testing a parameter change in general nonlinear integer-valued time series models where the conditional distribution of current observations is assumed to follow a one-parameter exponential family. We consider score-, (standardized) residual-, and estimate-based CUSUM tests and show that their limiting null distributions take the form of the functions of Brownian bridges. Based on the obtained results, we then conduct a comparison study of the performance of CUSUM tests through the use of Monte Carlo simulations. Our findings demonstrate that the standardized residual-based CUSUM test largely outperforms the others.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:71:y:2019:i:5:d:10.1007_s10463-018-0676-7
    DOI: 10.1007/s10463-018-0676-7
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    Cited by:

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    2. Huaping Chen & Qi Li & Fukang Zhu, 2022. "A new class of integer-valued GARCH models for time series of bounded counts with extra-binomial variation," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(2), pages 243-270, June.
    3. 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).

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