Non-stationary count time series characterized by features such as abrupt changes and fluctuations about the trend arise in many scientific domains including biophysics, ecology, energy, epidemiology, and social science domains. Current approaches for integer-valued time series lack the flexibility to capture local transient features while more flexible models for continuous data types are inadequate for universal applications to integer-valued responses such as settings with small counts. We present a modeling framework, the negative binomial Bayesian trend filter (NB-BTF), that offers an adaptive model-based solution to capturing multiscale features with valid integer-valued inference for trend filtering. The framework is a hierarchical Bayesian model with a dynamic global-local shrinkage process. The flexibility of the global-local process allows for the necessary local regularization while the temporal dependence induces a locally smooth trend. In simulation, the NB-BTF outperforms a number of alternative trend filtering methods. Then, we demonstrate the method on weekly power outage frequency in Massachusetts townships. Power outage frequency is characterized by a nominal low level with occasional spikes. These illustrations show the estimation of a smooth, non-stationary trend with adequate uncertainty quantification.

翻译：在许多科学领域，包括生物物理学、生态学、能源、流行病学和社会科学中，常出现具有突发变化和趋势波动等特征的非平稳计数时间序列。现有处理整数值时间序列的方法缺乏捕捉局部瞬态特征的灵活性，而适用于连续数据类型的更灵活模型无法普遍应用于整数值响应（如小计数场景）。我们提出一个建模框架——负二项式贝叶斯趋势滤波器（NB-BTF），该框架提供基于模型的自适应解决方案，用于捕捉多尺度特征并进行有效的整数值趋势滤波推理。该框架是一个具有动态全局-局部收缩过程的层次贝叶斯模型。全局-局部过程的灵活性允许必要的局部正则化，而时间依赖性则产生局部平滑的趋势。在模拟中，NB-BTF 优于多种替代趋势滤波方法。随后，我们将该方法应用于马萨诸塞州乡镇的每周停电频率数据。停电频率以低水平常态伴随偶发尖峰为特征。这些实例展示了在充分不确定性量化下对平滑非平稳趋势的估计。