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Bayesian Inference in High-Dimensional Time-varying Parameter Models using Integrated Rotated Gaussian Approximations

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  • Florian Huber
  • Gary Koop
  • Michael Pfarrhofer

Abstract

Researchers increasingly wish to estimate time-varying parameter (TVP) regressions which involve a large number of explanatory variables. Including prior information to mitigate over-parameterization concerns has led to many using Bayesian methods. However, Bayesian Markov Chain Monte Carlo (MCMC) methods can be very computationally demanding. In this paper, we develop computationally efficient Bayesian methods for estimating TVP models using an integrated rotated Gaussian approximation (IRGA). This exploits the fact that whereas constant coefficients on regressors are often important, most of the TVPs are often unimportant. Since Gaussian distributions are invariant to rotations we can split the the posterior into two parts: one involving the constant coefficients, the other involving the TVPs. Approximate methods are used on the latter and, conditional on these, the former are estimated with precision using MCMC methods. In empirical exercises involving artificial data and a large macroeconomic data set, we show the accuracy and computational benefits of IRGA methods.

Suggested Citation

  • Florian Huber & Gary Koop & Michael Pfarrhofer, 2020. "Bayesian Inference in High-Dimensional Time-varying Parameter Models using Integrated Rotated Gaussian Approximations," Papers 2002.10274, arXiv.org.
  • Handle: RePEc:arx:papers:2002.10274
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    References listed on IDEAS

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    Cited by:

    1. Niko Hauzenberger, 2020. "Flexible Mixture Priors for Large Time-varying Parameter Models," Papers 2006.10088, arXiv.org, revised Nov 2020.
    2. Hauzenberger, Niko, 2021. "Flexible Mixture Priors for Large Time-varying Parameter Models," Econometrics and Statistics, Elsevier, vol. 20(C), pages 87-108.
    3. Niko Hauzenberger & Florian Huber & Gary Koop, 2020. "Dynamic Shrinkage Priors for Large Time-varying Parameter Regressions using Scalable Markov Chain Monte Carlo Methods," Papers 2005.03906, arXiv.org.
    4. Yousuf, Kashif & Ng, Serena, 2021. "Boosting high dimensional predictive regressions with time varying parameters," Journal of Econometrics, Elsevier, vol. 224(1), pages 60-87.
    5. Michael Pfarrhofer, 2020. "Forecasts with Bayesian vector autoregressions under real time conditions," Papers 2004.04984, arXiv.org.

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