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An Adaptive Markov Chain Monte Carlo Method for GARCH Model

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  • Tetsuya Takaishi

Abstract

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.

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  • Tetsuya Takaishi, 2009. "An Adaptive Markov Chain Monte Carlo Method for GARCH Model," Papers 0901.0992, arXiv.org.
    • Handle: RePEc:arx:papers:0901.0992
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    Citations

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    Cited by:

    1. Tetsuya Takaishi, 2017. "Statistical properties and multifractality of Bitcoin," Papers 1707.07618, arXiv.org, revised May 2018.
    2. Tetsuya Takaishi, 2014. "Analysis of Spin Financial Market by GARCH Model," Papers 1409.0118, arXiv.org.
    3. Ting Ting Chen & Tetsuya Takaishi, 2013. "Empirical Study of the GARCH model with Rational Errors," Papers 1312.7057, arXiv.org.
    4. Li, Dan & Clements, Adam & Drovandi, Christopher, 2021. "Efficient Bayesian estimation for GARCH-type models via Sequential Monte Carlo," Econometrics and Statistics, Elsevier, vol. 19(C), pages 22-46.
    5. Takaishi, Tetsuya, 2018. "Statistical properties and multifractality of Bitcoin," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 507-519.
    6. Takaishi, Tetsuya, 2017. "Rational GARCH model: An empirical test for stock returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 451-460.
    7. Tetsuya Takaishi, 2013. "Empirical Analysis of Stochastic Volatility Model by Hybrid Monte Carlo Algorithm," Papers 1305.3184, arXiv.org.

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