The ARR2 prior: flexible predictive prior definition for Bayesian auto-regressions

TL;DR

The paper introduces the ARR2 prior, a flexible Bayesian prior for auto-regressive models that enhances inference quality and predictive performance, demonstrated through simulations and real-world data.

Contribution

The ARR2 prior is a novel, adaptable prior for Bayesian auto-regressions, extending to models with exogenous inputs and state-space frameworks, improving inference and prediction.

Findings

ARR2 prior outperforms existing priors in sparse inference

Demonstrates improved predictive accuracy in real-world datasets

Provides an open-source implementation for practical use

Abstract

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.