We present the ARR2 prior, a joint prior over the auto-regressive components in Bayesian time-series models and their induced $R^2$. Compared to other priors designed for times-series models, the ARR2 prior allows for flexible and intuitive shrinkage. We derive the prior for pure auto-regressive models, and extend it to auto-regressive models with exogenous inputs, and state-space models. Through both simulations and real-world modelling exercises, we demonstrate the efficacy of the ARR2 prior in improving sparse and reliable inference, while showing greater inference quality and predictive performance than other shrinkage priors. An open-source implementation of the prior is provided.

翻译：本文提出ARR2先验，这是一种针对贝叶斯时间序列模型中自回归分量及其诱导$R^2$的联合先验。相较于其他为时间序列模型设计的先验，ARR2先验能够实现更灵活且符合直觉的收缩效应。我们推导了该先验在纯自回归模型中的形式，并将其扩展至带外生输入的自回归模型以及状态空间模型。通过仿真实验与真实世界建模案例，我们证明了ARR2先验在提升稀疏性与推断可靠性方面的有效性，同时展现出优于其他收缩先验的推断质量与预测性能。文中提供了该先验的开源实现。