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.

这项研究提出了一类非线性滞后整数值GARCH模型，以通过三个气象协变量来描述每周登革热出血热病例的发生：降水，平均温度和相对湿度。提出的模型采用具有缓冲区的滞后三态切换机制，能够解释各种特性。这允许在较低状态中具有连续的零，并在较高状态中出现大量计数。这些非线性滞后整数值GARCH模型包括泊松，负二项式和对数链接形式。我们利用自适应马尔可夫链蒙特卡罗模拟进行推论和预测，并采用两个贝叶斯准则进行模型比较，并采用相对均方根预测误差进行评估。