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

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  • David Kohns
  • Noa Kallioinen
  • Yann McLatchie
  • Aki Vehtari

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.

Suggested Citation

  • David Kohns & Noa Kallioinen & Yann McLatchie & Aki Vehtari, 2024. "The ARR2 prior: flexible predictive prior definition for Bayesian auto-regressions," Papers 2405.19920, arXiv.org, revised May 2024.
  • Handle: RePEc:arx:papers:2405.19920
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    References listed on IDEAS

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    1. James H. Stock & Mark W. Watson, 2007. "Why Has U.S. Inflation Become Harder to Forecast?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(s1), pages 3-33, February.
    2. Yan Dora Zhang & Brian P. Naughton & Howard D. Bondell & Brian J. Reich, 2022. "Bayesian Regression Using a Prior on the Model Fit: The R2-D2 Shrinkage Prior," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(538), pages 862-874, April.
    3. Eric Yanchenko & Howard D. Bondell & Brian J. Reich, 2024. "Spatial regression modeling via the R2D2 framework," Environmetrics, John Wiley & Sons, Ltd., vol. 35(2), March.
    4. Zhang, Xiang & Saelens, Dirk & Roels, Staf, 2022. "Estimating dynamic solar gains from on-site measured data: An ARX modelling approach," Applied Energy, Elsevier, vol. 321(C).
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