Zero Variance and Hamiltonian Monte Carlo Methods in GARCH Models

Paixão, Rafael S.; Ehlers, Ricardo S.

doi:10.48550/arxiv.1710.07693

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2022

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“…Hence, the HMC algorithm has been introduced for inferring the time series models. For instance, Paixão and Ehlers (2017) used the HMC algorithm to estimate the GJR-GARCH model proposed by Glosten et al (1993) with normal and t-Student errors. Burda and Bélisle (2019) applied HMC algorithm to overcome the difficulty of inferring the Copula-GARCH model, of which the distribution of parameters is skewness, asymmetry and truncation.…”

Section: Introductionmentioning

confidence: 99%

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

2022

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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.

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Section: Introductionmentioning

confidence: 99%