  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.
