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Estimating the GARCH Diffusion: Simulated Maximum Likelihood in Continuous Time

Author

Listed:
  • Tore Selland Kleppe

    (Department of Mathematics, University of Bergen)

  • Jun Yu

    (School of Economics, Singapore Management University)

  • Hans J. Skaug

    (Department of Mathematics, University of Bergen)

Abstract

A new algorithm is developed to provide a simulated maximum likelihood estimation of the GARCH diffusion model of Nelson (1990) based on return data only. The method combines two accurate approximation procedures, namely, the polynomial expansion of Aït-Sahalia (2008) to approximate the transition probability density of return and volatility, and the Efficient Importance Sampler (EIS) of Richard and Zhang (2007) to integrate out the volatility. The first and second order terms in the polynomial expansion are used to generate a base-line importance density for an EIS algorithm. The higher order terms are included when evaluating the importance weights. Monte Carlo experiments show that the new method works well and the discretization error is well controlled by the polynomial expansion. In the empirical application, we fit the GARCH diffusion to equity data, perform diagnostics on the model fit, and test the finiteness of the importance weights.

Suggested Citation

  • Tore Selland Kleppe & Jun Yu & Hans J. Skaug, 2010. "Estimating the GARCH Diffusion: Simulated Maximum Likelihood in Continuous Time," Working Papers 13-2010, Singapore Management University, School of Economics.
    • Handle: RePEc:siu:wpaper:13-2010
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    File URL: https://mercury.smu.edu.sg/rsrchpubupload/17831/sml_garchdiffusion01.pdf
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    References listed on IDEAS

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    1. Ai[dieresis]t-Sahalia, Yacine & Yu, Jialin, 2006. "Saddlepoint approximations for continuous-time Markov processes," Journal of Econometrics, Elsevier, vol. 134(2), pages 507-551, October.
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    Cited by:

    1. Hafner, Christian M. & Laurent, Sebastien & Violante, Francesco, 2017. "Weak Diffusion Limits Of Dynamic Conditional Correlation Models," Econometric Theory, Cambridge University Press, vol. 33(3), pages 691-716, June.

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    More about this item

    Keywords

    Ecient importance sampling; GARCH diusion model; Simulated Maximum likelihood; Stochastic volatility;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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