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A Note on Efficient Fitting of Stochastic Volatility Models

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  • Chen Gong
  • David S. Stoffer

Abstract

The stochastic volatility model is a popular tool for modeling the volatility of assets. The model is a nonlinear and non‐Gaussian state space model and presents some challenges not seen in general. Many approaches have been developed for Bayesian analysis that rely on numerically intensive techniques such as Markov chain Monte Carlo (MCMC). Convergence and mixing problems still plague MCMC algorithms used for the model. We present an approach that ameliorates the slow convergence and mixing problems when fitting stochastic volatility models. The approach accelerates the convergence by exploiting the geometry of one of the targets. We demonstrate the method on various numerical examples.

Suggested Citation

  • Chen Gong & David S. Stoffer, 2021. "A Note on Efficient Fitting of Stochastic Volatility Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(2), pages 186-200, March.
    • Handle: RePEc:bla:jtsera:v:42:y:2021:i:2:p:186-200
    DOI: 10.1111/jtsa.12561
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    References listed on IDEAS

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    1. Kastner, Gregor & Frühwirth-Schnatter, Sylvia, 2014. "Ancillarity-sufficiency interweaving strategy (ASIS) for boosting MCMC estimation of stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 408-423.
    2. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
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    4. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    5. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 145-175.
    6. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-417, October.
    7. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342, June.
    8. Fredrik Lindsten & Randal Douc & Eric Moulines, 2015. "Uniform Ergodicity of the Particle Gibbs Sampler," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 775-797, September.
    9. Stephen J. Taylor, 1994. "Modeling Stochastic Volatility: A Review And Comparative Study," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 183-204, April.
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    Cited by:

    1. Raanju R. Sundararajan & Wagner Barreto‐Souza, 2023. "Student‐t stochastic volatility model with composite likelihood EM‐algorithm," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(1), pages 125-147, January.

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