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Bayesian Inference for Mixed Gaussian GARCH-Type Model by Hamiltonian Monte Carlo Algorithm.

Rubing Liang1, Binbin Qin1, Qiang Xia1

  • 1College of Mathematics and Informatics, South China Agricultural University, Guangzhou, 510642 People's Republic of China.

Computational Economics
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Hamiltonian Monte Carlo (HMC) algorithm offers efficient parameter estimation for Gaussian mixed GARCH-type models. This method improves volatility forecasting accuracy and flexibility compared to existing samplers.

Keywords:
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Area of Science:

  • Econometrics
  • Computational Statistics

Background:

  • Markov Chain Monte Carlo (MCMC) algorithms are standard for GARCH model parameter estimation.
  • Existing MCMC methods can be complex to implement and computationally intensive.

Purpose of the Study:

  • To introduce the Hamiltonian Monte Carlo (HMC) algorithm for parameter estimation in Gaussian mixed GARCH-type models.
  • To assess the performance of HMC for volatility forecasting.

Main Methods:

  • Application of the Hamiltonian Monte Carlo (HMC) algorithm for parameter estimation.
  • Volatility forecasting using HMC-derived posterior distributions.
  • Comparison with the Griddy-Gibbs sampler through simulation experiments.

Main Results:

  • HMC algorithm demonstrates superior efficiency and flexibility over the Griddy-Gibbs sampler.
  • HMC provides more accurate credibility intervals for volatility forecasting.
  • A real-world application validates the practical utility of the HMC approach.

Conclusions:

  • HMC is a viable and effective alternative for parameter estimation in GARCH models.
  • The proposed method enhances the accuracy and reliability of volatility predictions.
  • HMC offers practical advantages for financial econometrics applications.