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Bayesian inference of nonlinear hysteretic integer-valued GARCH models for disease counts

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Abstract

This study proposes a class of nonlinear hysteretic integer-valued GARCH models in order to describe the occurrence of weekly dengue hemorrhagic fever cases via three meteorological covariates: precipitation, average temperature, and relative humidity. The proposed model adopts the hysteretic three-regime switching mechanism with a buffer zone that are able to explain various characteristics. This allows for having consecutive zeros in the lower regime and large counts to appear up in the upper regime. These nonlinear hysteretic integer-valued GARCH models include Poisson, negative binomial, and log-linked forms. We utilize adaptive Markov chain Monte Carlo simulations for making inferences and prediction and employ two Bayesian criteria for model comparisons and the relative root mean squared prediction error for evaluation. Simulation and analytic results emphasize that the hysteretic negative binomial integer-valued GARCH model is superior to other models and successfully offers an alternative nonlinear integer-valued GARCH model to better describe larger values of counts.

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Acknowledgements

We thank the Editor, the Associate Editor, and anonymous referees for their valuable time and careful comments, which have helped improve this paper. Cathy W.S. Chen’s research is funded by the Ministry of Science and Technology, Taiwan (MOST107-2118-M-035-005-MY2). 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. 2018R1A2A2A05019433).

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Authors and Affiliations

  1. Department of Statistics, Feng Chia University, Taichung, Taiwan

    Cathy W. S. Chen & K. Khamthong

  2. Department of Statistics, Seoul National University, Seoul, Korea

    Sangyeol Lee

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  1. Cathy W. S. Chen
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  2. Sangyeol Lee
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  3. K. Khamthong
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Correspondence to Cathy W. S. Chen.

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Chen, C.W.S., Lee, S. & Khamthong, K. Bayesian inference of nonlinear hysteretic integer-valued GARCH models for disease counts. Comput Stat 36, 261–281 (2021). https://doi.org/10.1007/s00180-020-01018-7

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  • DOI: https://doi.org/10.1007/s00180-020-01018-7

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