Estimating the GARCH Diffusion: Simulated Maximum Likelihood in Continuous Time

Tore Kleppe (), Jun Yu and Hans J. Skaug ()
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Hans J. Skaug: Department of Mathematics, University of Bergen

No 13-2010, Working Papers from Singapore Management University, School of Economics

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.

Keywords: Ecient importance sampling; GARCH diusion model; Simulated Maximum likelihood; Stochastic volatility (search for similar items in EconPapers)
JEL-codes: C11 C15 G12 (search for similar items in EconPapers)
Pages: 35 pages
Date: 2010-01
New Economics Papers: this item is included in nep-ecm, nep-ets, nep-mic and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Published in SMU Economics and Statistics Working Paper Series

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