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Bayesian estimation of GARCH model with an adaptive proposal density
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"... Abstract A Bayesian estimation of a GARCH model is performed for US Dollar/Japanese Yen exchange rate by the MetropolisHastings algorithm with a proposal density given by the adaptive construction scheme. In the adaptive construction scheme the proposal density is assumed to take a form of a multiv ..."
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Abstract A Bayesian estimation of a GARCH model is performed for US Dollar/Japanese Yen exchange rate by the MetropolisHastings algorithm with a proposal density given by the adaptive construction scheme. In the adaptive construction scheme the proposal density is assumed to take a form of a multivariate Student’s tdistribution and its parameters are evaluated by using the sampled data and updated adaptively during Markov Chain Monte Carlo simulations. We find that the autocorrelation times between the data sampled by the adaptive construction scheme are considerably reduced. We conclude that the adaptive construction scheme works efficiently for the Bayesian inference of the GARCH model.
2009 Bayesian Inference on QGARCH Model Using the Adaptive Construction Scheme
 Proceedings of 8th IEEE/ACIS International Conference on Computer and Information Science 525 doi:10.1109/ICIS.2009.173
"... 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 MetropolisHastings algorithm is constructed adaptively by changing ..."
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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 MetropolisHastings 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. 1.
Bayesian inference with an adaptive proposal density for GARCH models
, 908
"... Abstract. We perform the Bayesian inference of a GARCH model by the MetropolisHastings algorithm with an adaptive proposal density. The adaptive proposal density is assumed to be the Student’s tdistribution and the distribution parameters are evaluated by using the data sampled during the simulati ..."
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Abstract. We perform the Bayesian inference of a GARCH model by the MetropolisHastings algorithm with an adaptive proposal density. The adaptive proposal density is assumed to be the Student’s tdistribution 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. 1.
Propagation of Error
"... • Any measuring procedure contains error – This causes measured values to differ from the true values that are measured • Errors in measurement produce error in calculated ..."
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• Any measuring procedure contains error – This causes measured values to differ from the true values that are measured • Errors in measurement produce error in calculated
Markov Chain Monte Carlo on Asymmetric GARCH Model Using the Adaptive Construction Scheme
, 909
"... Abstract. We perform Markov chain Monte Carlo simulations for a Bayesian inference of the GJRGARCH model which is one of asymmetric GARCH models. The adaptive construction scheme is used for the construction of the proposal density in the MetropolisHastings algorithm and the parameters of the prop ..."
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Abstract. We perform Markov chain Monte Carlo simulations for a Bayesian inference of the GJRGARCH model which is one of asymmetric GARCH models. The adaptive construction scheme is used for the construction of the proposal density in the MetropolisHastings algorithm and the parameters of the proposal density are determined adaptively by using the data sampled by the Markov chain Monte Carlo simulation. We study the performance of the scheme with the artificial GJRGARCH data. We find that the adaptive construction scheme samples GJRGARCH parameters effectively and conclude that the MetropolisHastings algorithm with the adaptive construction scheme is an efficient method to the Bayesian inference of the GJRGARCH model.
Empirical Analysis of Stochastic Volatility Model by Hybrid Monte Carlo Algorithm
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