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Data cloning estimation of GARCH and COGARCH models

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  • Rodríguez Bernal, M. T.
  • Marín Díazaraque, Juan Miguel
  • Romero, Eva

Abstract

GARCH models include most of the stylized facts of financial time series and they have been largely used to analyze discrete financial time series. In the last years, continuous time models based on discrete GARCH models have been also proposed to deal with non-equally spaced observations, as COGARCH model based on Lévy processes. In this paper, we propose to use the data cloning methodology in order to obtain estimators of GARCH and COGARCH model parameters. Data cloning methodology uses a Bayesian approach to obtain approximate maximum likelihood estimators avoiding numerically maximization of the pseudo-likelihood function. After a simulation study for both GARCH and COGARCH models using data cloning, we apply this technique to model the behavior of some NASDAQ time series

Suggested Citation

  • Rodríguez Bernal, M. T. & Marín Díazaraque, Juan Miguel & Romero, Eva, 2013. "Data cloning estimation of GARCH and COGARCH models," DES - Working Papers. Statistics and Econometrics. WS ws132723, Universidad Carlos III de Madrid. Departamento de Estadística.
  • Handle: RePEc:cte:wsrepe:ws132723
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    References listed on IDEAS

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    3. Jan Kallsen & Murad S. Taqqu, 1998. "Option Pricing in ARCH-type Models," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 13-26.
    4. Lele, Subhash R. & Nadeem, Khurram & Schmuland, Byron, 2010. "Estimability and Likelihood Inference for Generalized Linear Mixed Models Using Data Cloning," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1617-1625.
    5. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    6. Gernot Müller, 2010. "MCMC Estimation of the COGARCH(1,1) Model," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 8(4), pages 481-510, Fall.
    7. Godfrey, Leslie G, 1978. "Testing against General Autoregressive and Moving Average Error Models When the Regressors Include Lagged Dependent Variables," Econometrica, Econometric Society, vol. 46(6), pages 1293-1301, November.
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    12. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
    13. repec:spr:lnecms:978-3-540-78657-3 is not listed on IDEAS
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    Keywords

    MCMC algorithm;

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