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An Adaptive Markov Chain Monte Carlo Method for GARCH Model

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  • Tetsuya Takaishi
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    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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    File URL: http://arxiv.org/pdf/0901.0992
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 0901.0992.

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    Date of creation: Jan 2009
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    Publication status: Published in Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering. Complex Sciences, vol. 5 (2009) 1424-1434
    Handle: RePEc:arx:papers:0901.0992

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    Web page: http://arxiv.org/

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    1. Kaizoji, Taisei & Bornholdt, Stefan & Fujiwara, Yoshi, 2002. "Dynamics of price and trading volume in a spin model of stock markets with heterogeneous agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 441-452.
    2. Tetsuya Takaishi, 2005. "Simulations of financial markets in a Potts-like model," Papers cond-mat/0503156, arXiv.org.
    3. Bauwens, L. & Lubrano, M., . "Bayesian inference on GARCH models using the Gibbs sampler," CORE Discussion Papers RP -1307, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. K. Sznajd-Weron & R. Weron, 2000. "A simple model of price formation," Papers cond-mat/0101001, arXiv.org, revised Nov 2001.
    5. Sangjoon Kim, Neil Shephard & Siddhartha Chib, . "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers W26, revised version of W, Economics Group, Nuffield College, University of Oxford.
    6. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    8. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    9. Nakatsuma, Teruo, 2000. "Bayesian analysis of ARMA-GARCH models: A Markov chain sampling approach," Journal of Econometrics, Elsevier, vol. 95(1), pages 57-69, March.
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    Cited by:
    1. Tetsuya Takaishi, 2013. "Empirical Analysis of Stochastic Volatility Model by Hybrid Monte Carlo Algorithm," Papers 1305.3184, arXiv.org.
    2. Ting Ting Chen & Tetsuya Takaishi, 2013. "Empirical Study of the GARCH model with Rational Errors," Papers 1312.7057, arXiv.org.

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