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Data cloning estimation of GARCH and COGARCH models

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  • J. Miguel Marín

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  • M. T. Rodríguez Bernal

    ()

  • Eva Romero

    ()

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    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

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    Bibliographic Info

    Paper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws132723.

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    Date of creation: Jul 2013
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    Handle: RePEc:cte:wsrepe:ws132723

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    Related research

    Keywords: GARCH; Continuous-time GARCH process; Lévy process; COGARCH; Data cloning; Bayesian inference; MCMC algorithm;

    This paper has been announced in the following NEP Reports:

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    1. 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.
    2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    3. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
    4. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, School of Economics and Management, University of Aarhus.
    5. Jan Kallsen & Murad S. Taqqu, 1998. "Option Pricing in ARCH-type Models," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 13-26.
    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.
    8. Nakatsuma Teruo, 1998. "A Markov-Chain Sampling Algorithm for GARCH Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 3(2), pages 1-13, July.
    9. 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.
    10. Ross A. Maller & Gernot M\"uller & Alex Szimayer, 2008. "GARCH modelling in continuous time for irregularly spaced time series data," Papers 0805.2096, arXiv.org.
    11. Corradi, Valentina, 2000. "Reconsidering the continuous time limit of the GARCH(1, 1) process," Journal of Econometrics, Elsevier, vol. 96(1), pages 145-153, May.
    12. S. Haug & C. Kl�ppelberg & A. Lindner & M. Zapp, 2007. "Method of moment estimation in the COGARCH(1,1) model," Econometrics Journal, Royal Economic Society, vol. 10(2), pages 320-341, 07.
    13. Breusch, T S, 1978. "Testing for Autocorrelation in Dynamic Linear Models," Australian Economic Papers, Wiley Blackwell, vol. 17(31), pages 334-55, December.
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