IDEAS home Printed from https://ideas.repec.org/p/arx/papers/0901.0992.html
   My bibliography  Save this paper

An Adaptive Markov Chain Monte Carlo Method for GARCH Model

Author

Listed:
  • 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.

Suggested Citation

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

    Download full text from publisher

    File URL: http://arxiv.org/pdf/0901.0992
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. K. Sznajd-Weron & R. Weron, 2002. "A Simple Model Of Price Formation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 13(01), pages 115-123.
    2. Takuya Yamano, 2002. "A Spin Model Of Market Dynamics With Random Nearest Neighbor Coupling," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 13(05), pages 645-648.
    3. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. Luc Bauwens & Michel Lubrano, 1998. "Bayesian inference on GARCH models using the Gibbs sampler," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages 23-46.
    6. 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.
    7. 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.
    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. Tetsuya Takaishi, 2005. "Simulations Of Financial Markets In A Potts-Like Model," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 16(08), pages 1311-1317.
    10. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    11. Juan R. Sanchez, 2002. "A Simple Model For Stocks Markets," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 13(05), pages 639-644.
    12. Tetsuya Takaishi, 2005. "Simulations of financial markets in a Potts-like model," Papers cond-mat/0503156, arXiv.org.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. Ting Ting Chen & Tetsuya Takaishi, 2013. "Empirical Study of the GARCH model with Rational Errors," Papers 1312.7057, arXiv.org.
    4. Tetsuya Takaishi, 2013. "Empirical Analysis of Stochastic Volatility Model by Hybrid Monte Carlo Algorithm," Papers 1305.3184, arXiv.org.
    5. Tetsuya Takaishi, 2017. "Statistical properties and multifractality of Bitcoin," Papers 1707.07618, arXiv.org, revised May 2018.
    6. Tetsuya Takaishi, 2014. "Analysis of Spin Financial Market by GARCH Model," Papers 1409.0118, arXiv.org.
    7. Takaishi, Tetsuya, 2018. "Statistical properties and multifractality of Bitcoin," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 507-519.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tetsuya Takaishi, 2008. "Financial Time Series Analysis of SV Model by Hybrid Monte Carlo," Papers 0807.4394, arXiv.org.
    2. Tetsuya Takaishi, 2014. "Analysis of Spin Financial Market by GARCH Model," Papers 1409.0118, arXiv.org.
    3. Tetsuya Takaishi, 2009. "Markov Chain Monte Carlo on Asymmetric GARCH Model Using the Adaptive Construction Scheme," Papers 0909.1478, arXiv.org.
    4. Tetsuya Takaishi, 2016. "Dynamical cross-correlation of multiple time series Ising model," Evolutionary and Institutional Economics Review, Springer, vol. 13(2), pages 455-468, December.
    5. Audrone Virbickaite & M. Concepción Ausín & Pedro Galeano, 2015. "Bayesian Inference Methods For Univariate And Multivariate Garch Models: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 29(1), pages 76-96, February.
    6. Gabriele Fiorentini & Enrique Sentana & Neil Shephard, 2004. "Likelihood-Based Estimation of Latent Generalized ARCH Structures," Econometrica, Econometric Society, vol. 72(5), pages 1481-1517, September.
    7. Xibin Zhang & Maxwell L. King, 2011. "Bayesian semiparametric GARCH models," Monash Econometrics and Business Statistics Working Papers 24/11, Monash University, Department of Econometrics and Business Statistics.
    8. Xibin Zhang & Maxwell L. King, 2013. "Gaussian kernel GARCH models," Monash Econometrics and Business Statistics Working Papers 19/13, Monash University, Department of Econometrics and Business Statistics.
    9. Aknouche, Abdelhakim & Demmouche, Nacer & Touche, Nassim, 2018. "Bayesian MCMC analysis of periodic asymmetric power GARCH models," MPRA Paper 91136, University Library of Munich, Germany.
    10. Zhang, Bo & Chan, Joshua C.C. & Cross, Jamie L., 2020. "Stochastic volatility models with ARMA innovations: An application to G7 inflation forecasts," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1318-1328.
    11. Zhang, Xibin & King, Maxwell L., 2008. "Box-Cox stochastic volatility models with heavy-tails and correlated errors," Journal of Empirical Finance, Elsevier, vol. 15(3), pages 549-566, June.
    12. Hoogerheide, Lennart & van Dijk, Herman K., 2010. "Bayesian forecasting of Value at Risk and Expected Shortfall using adaptive importance sampling," International Journal of Forecasting, Elsevier, vol. 26(2), pages 231-247, April.
    13. Kei Katahira & Yu Chen, 2019. "Heterogeneous wealth distribution, round-trip trading and the emergence of volatility clustering in Speculation Game," Papers 1909.03185, arXiv.org.
    14. Kei Katahira & Yu Chen & Gaku Hashimoto & Hiroshi Okuda, 2019. "Development of an agent-based speculation game for higher reproducibility of financial stylized facts," Papers 1902.02040, arXiv.org.
    15. So, Mike K.P. & Chen, Cathy W.S. & Lee, Jen-Yu & Chang, Yi-Ping, 2008. "An empirical evaluation of fat-tailed distributions in modeling financial time series," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(1), pages 96-108.
    16. Charles S. Bos & Ronald J. Mahieu & Herman K. Van Dijk, 2000. "Daily exchange rate behaviour and hedging of currency risk," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(6), pages 671-696.
    17. Liu, Zhenya & Wang, Shixuan, 2017. "Decoding Chinese stock market returns: Three-state hidden semi-Markov model," Pacific-Basin Finance Journal, Elsevier, vol. 44(C), pages 127-149.
    18. Miazhynskaia, Tatiana & Fruhwirth-Schnatter, Sylvia & Dorffner, Georg, 2006. "Bayesian testing for non-linearity in volatility modeling," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 2029-2042, December.
    19. Ausin, Maria Concepcion & Galeano, Pedro, 2007. "Bayesian estimation of the Gaussian mixture GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2636-2652, February.
    20. Tatiana Miazhynskaia & Georg Dorffner, 2006. "A comparison of Bayesian model selection based on MCMC with an application to GARCH-type models," Statistical Papers, Springer, vol. 47(4), pages 525-549, October.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:0901.0992. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.