Dynamic Linear Models (DLMs) are commonly employed for time series analysis due to their versatile structure, simple recursive updating, and probabilistic forecasting. However, the options for count time series are limited: Gaussian DLMs require continuous data, while Poisson-based alternatives often lack sufficient modeling flexibility. We introduce a novel methodology for count time series by warping a Gaussian DLM. The warping function has two components: a transformation operator that provides distributional flexibility and a rounding operator that ensures the correct support for the discrete data-generating process. Importantly, we develop conjugate inference for the warped DLM, which enables analytic and recursive updates for the state space filtering and smoothing distributions. We leverage these results to produce customized and efficient computing strategies for inference and forecasting, including Monte Carlo simulation for offline analysis and an optimal particle filter for online inference. This framework unifies and extends a variety of discrete time series models and is valid for natural counts, rounded values, and multivariate observations. Simulation studies illustrate the excellent forecasting capabilities of the warped DLM. The proposed approach is applied to a multivariate time series of daily overdose counts and demonstrates both modeling and computational successes.
翻译:动态线性模型(DLMS)通常用于时间序列分析,因为其多功能结构、简单的循环更新和概率预测。然而,计算时间序列的选择有限:高山DLMS需要连续数据,而以Poisson为基础的替代品往往缺乏足够的建模灵活性。我们引入了一种新的计时时间序列方法,对高山DLM进行扭曲。扭曲功能有两个组成部分:一个提供分配灵活性的转换操作器和一个圆形操作器,以确保对离散数据生成过程的正确支持。重要的是,我们为扭曲的DLM(DLM)开发了二次推论,为州空间过滤和平滑分布提供了分析和递现更新。我们利用这些结果来生成定制和高效的推断和预测计算战略,包括用于离线分析的蒙特卡洛模拟和用于在线推断的最佳粒子过滤器。这个框架统一和扩展了各种离散时间序列模型,对于自然计数、四舍值和多变量观测是有效的。模拟模型的模拟研究为州空间过滤和平滑动分配的每日测算法展示了优劣的模型。