This study focuses on modelling dengue cases in northeastern Thailand through two meteorological covariates: cumulative rainfall and average maximum temperature. We propose two nonlinear integer-valued GARCHX models (Markov switching and threshold specification) with a negative binomial distribution, as they take into account the stylized features of weekly dengue haemorrhagic fever cases, which contain nonlinear dynamics, lagged dependence, overdispersion, consecutive zeros and asymmetric effects of meteorological covariates. We conduct parameter estimation and one-step-ahead forecasting for two proposed models based on Bayesian Markov chain Monte Carlo (MCMC) methods. A simulation study illustrates that the adaptive MCMC sampling scheme performs well. The empirical results offer strong support for the Markov switching integer-valued GARCHX model over its competitors via Bayes factor and deviance information criterion. We also provide one-step-ahead forecasting based on the prediction interval that offers a useful early warning signal of outbreak detection.

中文翻译：

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非线性负二项式整数值 GARCHX 模型的贝叶斯建模

本研究的重点是通过两个气象协变量对泰国东北部的登革热病例进行建模：累积降雨量和平均最高温度。我们提出了两个具有负二项分布的非线性整数值 GARCHX 模型（马尔可夫切换和阈值规范），因为它们考虑了每周登革出血热病例的程式化特征，其中包含非线性动力学、滞后依赖性、过度分散、连续零和气象协变量的不对称效应。我们基于贝叶斯马尔可夫链蒙特卡罗 (MCMC) 方法对两个提出的模型进行参数估计和一步超前预测。仿真研究表明自适应 MCMC 采样方案表现良好。实证结果通过贝叶斯因子和偏差信息标准为马尔可夫转换整数值 GARCHX 模型提供了强有力的支持。我们还提供基于预测间隔的提前一步预测，该预测间隔提供了有用的爆发检测预警信号。