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Predictions with dynamic Bayesian predictive synthesis are exact minimax

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  • K=osaku Takanashi
  • Kenichiro McAlinn

Abstract

We analyze the combination of multiple predictive distributions for time series data when all forecasts are misspecified. We show that a specific dynamic form of Bayesian predictive synthesis -- a general and coherent Bayesian framework for ensemble methods -- produces exact minimax predictive densities with regard to Kullback-Leibler loss, providing theoretical support for finite sample predictive performance over existing ensemble methods. A simulation study that highlights this theoretical result is presented, showing that dynamic Bayesian predictive synthesis is superior to other ensemble methods using multiple metrics.

Suggested Citation

  • K=osaku Takanashi & Kenichiro McAlinn, 2019. "Predictions with dynamic Bayesian predictive synthesis are exact minimax," Papers 1911.08662, arXiv.org, revised Jul 2021.
  • Handle: RePEc:arx:papers:1911.08662
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    References listed on IDEAS

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    Cited by:

    1. Knut Are Aastveit & Jamie Cross & Herman K. van Dijk, 2021. "Quantifying time-varying forecast uncertainty and risk for the real price of oil," Tinbergen Institute Discussion Papers 21-053/III, Tinbergen Institute.
    2. Francis X. Diebold & Minchul Shin & Boyuan Zhang, 2020. "On the Aggregation of Probability Assessments: Regularized Mixtures of Predictive Densities for Eurozone Inflation and Real Interest Rates," Papers 2012.11649, arXiv.org, revised Jun 2022.
    3. Kenichiro McAlinn & Kosaku Takanashi, 2019. "Mean-shift least squares model averaging," Papers 1912.01194, arXiv.org.

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