This research proposes a comprehensive ALG model (Adaptive Log-linear zero-inflated Generalized Poisson integer-valued GARCH) to describe the dynamics of integer-valued time series of crime incidents with the features of autocorrelation, heteroscedasticity, overdispersion and excessive number of zero observations. The proposed ALG model captures time-varying nonlinear dependence and simultaneously incorporates the impact of multiple exogenous variables in a unified modeling framework. We use an adaptive approach to automatically detect subsamples of local homogeneity at each time point of interest and estimate the time-dependent parameters through an adaptive Bayesian Markov chain Monte Carlo (MCMC) sampling scheme. A simulation study shows stable and accurate finite sample performances of the ALG model under both homogeneous and heterogeneous scenarios. When implemented with data on crime incidents in Byron, Australia, the ALG model delivers a persuasive estimation of the stochastic intensity of criminal incidents and provides insightful interpretations on both the dynamics of intensity and the impacts of temperature and demographic factors for different crime categories.

中文翻译：

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自适应对数线性零膨胀广义泊松自回归模型及其在犯罪计数中的应用

这项研究提出了一个综合的ALG模型（自适应对数线性零膨胀广义Poisson整数值GARCH）来描述犯罪事件的整数值时间序列的动力学，具有自相关，异方差，过度分散和零观察数过多的特征。所提出的ALG模型捕获了时变的非线性依赖性，并同时将多个外生变量的影响合并到一个统一的建模框架中。我们使用一种自适应方法，在每个感兴趣的时间点自动检测局部均匀性的子样本，并通过自适应贝叶斯马尔可夫链蒙特卡洛（MCMC）采样方案来估计与时间有关的参数。仿真研究表明，在同质和异质场景下，ALG模型的稳定和准确的有限样本性能。如果将ALG模型与澳大利亚拜伦州的犯罪事件数据一起使用，则可以对犯罪事件的随机强度进行有说服力的估计，并就强度的动态以及温度和人口因素对不同犯罪类别的影响提供深刻的解释。