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

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  • Cathy W. S. Chen

    (Feng Chia University)

  • Sangyeol Lee

    (Seoul National University)

  • K. Khamthong

    (Feng Chia University)

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.

Suggested Citation

  • Cathy W. S. Chen & Sangyeol Lee & K. Khamthong, 2021. "Bayesian inference of nonlinear hysteretic integer-valued GARCH models for disease counts," Computational Statistics, Springer, vol. 36(1), pages 261-281, March.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:1:d:10.1007_s00180-020-01018-7
    DOI: 10.1007/s00180-020-01018-7
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    Cited by:

    1. Cathy W. S. Chen & Edward M. H. Lin & Tara F. J. Huang, 2022. "Bayesian quantile forecasting via the realized hysteretic GARCH model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(7), pages 1317-1337, November.
    2. Chen, Cathy W.S. & Liu, Feng-Chi & Pingal, Aljo Clair, 2023. "Integer-valued transfer function models for counts that show zero inflation," Statistics & Probability Letters, Elsevier, vol. 193(C).
    3. Chen, Cathy W.S. & Chen, Chun-Shu & Hsiung, Mo-Hua, 2023. "Bayesian modeling of spatial integer-valued time series," Computational Statistics & Data Analysis, Elsevier, vol. 188(C).

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