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Empirical Study of the GARCH model with Rational Errors

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  • Ting Ting Chen
  • Tetsuya Takaishi

Abstract

We use the GARCH model with a fat-tailed error distribution described by a rational function and apply it for the stock price data on the Tokyo Stock Exchange. To determine the model parameters we perform the Bayesian inference to the model. The Bayesian inference is implemented by the Metropolis-Hastings algorithm with an adaptive multi-dimensional Student's t-proposal density. In order to compare the model with the GARCH model with the standard normal errors we calculate information criterions: AIC and DIC, and find that both criterions favor the GARCH model with a rational error distribution. We also calculate the accuracy of the volatility by using the realized volatility and find that a good accuracy is obtained for the GARCH model with a rational error distribution. Thus we conclude that the GARCH model with a rational error distribution is superior to the GARCH model with the normal errors and it can be used as an alternative GARCH model to those with other fat-tailed distributions.

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  • Ting Ting Chen & Tetsuya Takaishi, 2013. "Empirical Study of the GARCH model with Rational Errors," Papers 1312.7057, arXiv.org.
  • Handle: RePEc:arx:papers:1312.7057
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    File URL: http://arxiv.org/pdf/1312.7057
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    3. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
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    5. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    6. Tetsuya Takaishi, 2009. "An Adaptive Markov Chain Monte Carlo Method for GARCH Model," Papers 0901.0992, arXiv.org.
    7. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
    8. Alderweireld, Thomas & Nuyts, Jean, 2004. "Detailed empirical study of the term structure of interest rates. Emergence of power laws and scaling laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 331(3), pages 602-616.
    9. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
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    11. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    12. 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.
    13. 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.
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    Cited by:

    1. 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.

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