Bayesian inference of nonlinear hysteretic integer-valued GARCH models for disease counts
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Bayesian inference of nonlinear hysteretic integer-valued GARCH models for disease counts Cathy W. S. Chen1
· Sangyeol Lee2
· K. Khamthong1
Received: 7 August 2019 / Accepted: 11 July 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
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. Keywords Dengue fever · Integer-valued GARCH · Overdispersion · Consecutive zeros · Hysteresis · MCMC method · Posterior predictive distribution · Threshold model
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00180020-01018-7) contains supplementary material, which is available to authorized users.
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Cathy W. S. Chen [email protected]
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Department of Statistics, Feng Chia University, Taichung, Taiwan
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Department of Statistics, Seoul National University, Seoul, Korea
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C. W. S. Chen et al.
1 Introduction Time series of counts are often collected in many areas, including epidemiology, economics, insurance, criminology, and accidents. Such data usually have nonnormal distributions and common overdispersion (where the mean is less than the variance). The literature has developed a class of integer-valued GARCH models and studied them for overdispersion over the past decade; see Ferland et al. (2006). Several papers present different integer-valued models with several distributions; i.e. Poisson and negative binomial distribution, see Fokianos and Tjøstheim (2011), Xu et al. (2012), and Chen et al. (2016). Many extensions appear in the literature; for example, to account for many zeros in the dataset, Lambert (1992), Jazi et al. (2012), Zhu (2012), Lee et al. (2016), and Chen and Lee (2016) focus on various zero-inflated (ZI) models to allow for frequent zero-valued time series of counts. Dengue is a common and serious mosquito-borne viral infection, in which confirmed dengue cases usually are counted on a weekly time frame. The purpose of this study is to model the occurrence of weekly dengue hemorrhagic fever (DHF) cases
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