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

Abstract

MCMC algorithm is widely used in parameters' estimation of GARCH-type models. However, the existing algorithms are either not easy to implement or not fast to run. In this paper, Hamiltonian Monte Carlo (HMC) algorithm, which is easy to perform and also efficient to draw samples from posterior distributions, is firstly proposed to estimate for the Gaussian mixed GARCH-type models. And then, based on the estimation of HMC algorithm, the forecasting of volatility prediction is investigated. Through the simulation experiments, the HMC algorithm is more efficient and flexible than the Griddy-Gibbs sampler, and the credibility interval of forecasting for volatility prediction is also more accurate. A real application is given to support the usefulness of the proposed HMC algorithm well.