Abstract
In this paper, we consider the problem of testing for a parameter change in bivariate Poisson integer-valued GARCH(1, 1) models, constructed via a trivariate reduction method of independent Poisson variables. We verify that the conditional maximum-likelihood estimator of the model parameters is asymptotically normal. Then, based on these results, we construct CMLE- and residual-based CUSUM tests and derive that their limiting null distributions are a function of independent Brownian bridges. A simulation study and real data analysis are conducted for illustration.
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Acknowledgements
We thank the Editor and the two anonymous referees for their careful reading and valuable comments to improve the quality of the paper. Sangyeol Lee’s research is supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and future Planning (No. 2015R1A2A2A010003894).
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Lee, Y., Lee, S. & Tjøstheim, D. Asymptotic normality and parameter change test for bivariate Poisson INGARCH models. TEST 27, 52–69 (2018). https://doi.org/10.1007/s11749-016-0510-6
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DOI: https://doi.org/10.1007/s11749-016-0510-6