1,113 research outputs found
An Adaptive Markov Chain Monte Carlo Method for GARCH Model
We propose a method to construct a proposal density for the
Metropolis-Hastings algorithm in Markov Chain Monte Carlo (MCMC) simulations of
the GARCH model. The proposal density is constructed adaptively by using the
data sampled by the MCMC metho d itself. It turns out that autocorrelations
between the data generated with our adaptive proposal density are greatly
reduced. Thus it is concluded that the adaptive construction method is very
efficient and works well for the MCMC simulations of the GARCH model.Comment: 11 pages, 6 figure
Bayesian Adaptive Hamiltonian Monte Carlo with an Application to High-Dimensional BEKK GARCH Models
Hamiltonian Monte Carlo (HMC) is a recent statistical procedure to sample from complex distributions. Distant proposal draws are taken in a equence of steps following the Hamiltonian dynamics of the underlying parameter space, often yielding superior mixing properties of the resulting Markov chain. However, its performance can deteriorate sharply with the degree of irregularity of the underlying likelihood due to its lack of local adaptability in the parameter space. Riemann Manifold HMC (RMHMC), a locally adaptive version of HMC, alleviates this problem, but at a substantially increased computational cost that can become prohibitive in high-dimensional scenarios. In this paper we propose the Adaptive HMC (AHMC), an alternative inferential method based on HMC that is both fast and locally adaptive, combining the advantages of both HMC and RMHMC. The benefits become more pronounced with higher dimensionality of the parameter space and with the degree of irregularity of the underlying likelihood surface. We show that AHMC satisfies detailed balance for a valid MCMC scheme and provide a comparison with RMHMC in terms of effective sample size, highlighting substantial efficiency gains of AHMC. Simulation examples and an application of the BEKK GARCH model show the usefulness of the new posterior sampler.High-dimensional joint sampling; Markov chain Monte Carlo; Multivariate GARCH
Bayesian Adaptive Hamiltonian Monte Carlo with an Application to High-Dimensional BEKK GARCH Models
Hamiltonian Monte Carlo (HMC) is a recent statistical procedure to sample from complex distributions. Distant proposal draws are taken in a equence of steps following the Hamiltonian dynamics of the underlying parameter space, often yielding superior mixing properties of the resulting Markov chain. However, its performance can deteriorate sharply with the degree of irregularity of the underlying likelihood due to its lack of local adaptability in the parameter space. Riemann Manifold HMC (RMHMC), a locally adaptive version of HMC, alleviates this problem, but at a substantially increased computational cost that can become prohibitive in high-dimensional scenarios. In this paper we propose the Adaptive HMC (AHMC), an alternative inferential method based on HMC that is both fast and locally adaptive, combining the advantages of both HMC and RMHMC. The benefits become more pronounced with higher dimensionality of the parameter space and with the degree of irregularity of the underlying likelihood surface. We show that AHMC satisfies detailed balance for a valid MCMC scheme and provide a comparison with RMHMC in terms of effective sample size, highlighting substantial efficiency gains of AHMC. Simulation examples and an application of the BEKK GARCH model show the usefulness of the new posterior sampler.High-dimensional joint sampling; Markov chain Monte Carlo; Multivariate GARCH
Bayesian Inference on QGARCH Model Using the Adaptive Construction Scheme
We study the performance of the adaptive construction scheme for a Bayesian
inference on the Quadratic GARCH model which introduces the asymmetry in time
series dynamics. In the adaptive construction scheme a proposal density in the
Metropolis-Hastings algorithm is constructed adaptively by changing the
parameters of the density to fit the posterior density. Using artificial QGARCH
data we infer the QGARCH parameters by applying the adaptive construction
scheme to the Bayesian inference of QGARCH model. We find that the adaptive
construction scheme samples QGARCH parameters effectively, i.e. correlations
between the sampled data are very small. We conclude that the adaptive
construction scheme is an efficient method to the Bayesian estimation of the
QGARCH model.Comment: ICIS200
Bayesian inference with an adaptive proposal density for GARCH models
We perform the Bayesian inference of a GARCH model by the Metropolis-Hastings
algorithm with an adaptive proposal density. The adaptive proposal density is
assumed to be the Student's t-distribution and the distribution parameters are
evaluated by using the data sampled during the simulation. We apply the method
for the QGARCH model which is one of asymmetric GARCH models and make empirical
studies for for Nikkei 225, DAX and Hang indexes. We find that autocorrelation
times from our method are very small, thus the method is very efficient for
generating uncorrelated Monte Carlo data. The results from the QGARCH model
show that all the three indexes show the leverage effect, i.e. the volatility
is high after negative observations
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