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Numerical integration-based Gaussian mixture filters for maximum likelihood estimation of asymmetric stochastic volatility models

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  • Hiroyuki Kawakatsu

Abstract

I consider Gaussian filters based on numerical integration for maximum likelihood estimation of stochastic volatility models with leverage. I show that for this class of models, the prediction step of the Gaussian filter can be evaluated analytically without linearizing the state--space model. Monte Carlo simulations show that the mixture Gaussian filter performs remarkably well in terms of both accuracy and computation time compared to the quasi-maximum likelihood and importance sampler filters. The result that the prediction step of the Gaussian filter can be evaluated analytically is shown to apply more generally to a number of commonly used specifications of the stochastic volatility model. Copyright Royal Economic Society 2007

Suggested Citation

  • Hiroyuki Kawakatsu, 2007. "Numerical integration-based Gaussian mixture filters for maximum likelihood estimation of asymmetric stochastic volatility models," Econometrics Journal, Royal Economic Society, vol. 10(2), pages 342-358, July.
    • Handle: RePEc:ect:emjrnl:v:10:y:2007:i:2:p:342-358
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    Cited by:

    1. Tore Selland Kleppe & Jun Yu & H.J. Skaug, 2010. "Simulated maximum likelihood estimation of continuous time stochastic volatility models," Advances in Econometrics, in: Maximum Simulated Likelihood Methods and Applications, pages 137-161, Emerald Group Publishing Limited.
    2. Almut Veraart, 2011. "How precise is the finite sample approximation of the asymptotic distribution of realised variation measures in the presence of jumps?," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(3), pages 253-291, September.
    3. Tore Selland Kleppe & Jun Yu & Hans J. Skaug, 2011. "Simulated Maximum Likelihood Estimation for Latent Diffusion Models," Working Papers CoFie-04-2011, Singapore Management University, Sim Kee Boon Institute for Financial Economics.
    4. Cai, Lili & Swanson, Norman R., 2011. "In- and out-of-sample specification analysis of spot rate models: Further evidence for the period 1982-2008," Journal of Empirical Finance, Elsevier, vol. 18(4), pages 743-764, September.
    5. Aït-Sahalia, Yacine & Li, Chenxu & Li, Chen Xu, 2024. "Maximum likelihood estimation of latent Markov models using closed-form approximations," Journal of Econometrics, Elsevier, vol. 240(2).
    6. Guillermo Avellán & Manuel González-Astudillo & Juan José Salcedo Cruz, 2022. "Measuring uncertainty: A streamlined application for the Ecuadorian economy," Empirical Economics, Springer, vol. 62(4), pages 1517-1542, April.
    7. Bretó, Carles & Veiga, Helena, 2011. "Forecasting volatility: does continuous time do better than discrete time?," DES - Working Papers. Statistics and Econometrics. WS ws112518, Universidad Carlos III de Madrid. Departamento de Estadística.

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