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Markov Chain Monte Carlo on Asymmetric GARCH Model Using the Adaptive Construction Scheme

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  • Tetsuya Takaishi
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    Abstract

    We perform Markov chain Monte Carlo simulations for a Bayesian inference of the GJR-GARCH model which is one of asymmetric GARCH models. The adaptive construction scheme is used for the construction of the proposal density in the Metropolis-Hastings 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 GJR-GARCH data. We find that the adaptive construction scheme samples GJR-GARCH parameters effectively and conclude that the Metropolis-Hastings algorithm with the adaptive construction scheme is an efficient method to the Bayesian inference of the GJR-GARCH model.

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    File URL: http://arxiv.org/pdf/0909.1478
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 0909.1478.

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    Date of creation: Sep 2009
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    Publication status: Published in Lecture Notes in Computer Science, 2009, Volume 5754/2009, 1112-1121
    Handle: RePEc:arx:papers:0909.1478

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    Web page: http://arxiv.org/

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    1. Bauwens, L. & Lubrano, M., 1996. "Bayesian Inference on GARCH Models Using the Gibbs Sampler," G.R.E.Q.A.M. 96a21, Universite Aix-Marseille III.
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    7. Tetsuya Takaishi, 2009. "Bayesian Inference on QGARCH Model Using the Adaptive Construction Scheme," Papers 0907.5276, arXiv.org.
    8. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
    9. Sentana, Enrique, 1995. "Quadratic ARCH Models," Review of Economic Studies, Wiley Blackwell, vol. 62(4), pages 639-61, October.
    10. 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.
    11. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
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