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Stochastic volatility: Bayesian computation using automatic differentiation and the extended Kalman filter

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  • Renate Meyer
  • David A. Fournier
  • Andreas Berg

Abstract

Stochastic volatility (SV) models provide more realistic and flexible alternatives to ARCH-type models for describing time-varying volatility exhibited in many financial time series. They belong to the wide class of nonlinear state-space models. As classical parameter estimation for SV models is difficult due to the intractable form of the likelihood, Bayesian approaches using Markov chain Monte Carlo (MCMC) techniques for posterior computations have been suggested. In this paper, an efficient MCMC algorithm for posterior computation in SV models is presented. It is related to the integration sampler of Kim et al.(1998) but does not need an offset mixture of normals approximation to the likelihood. Instead, the extended Kalman Filter is combined with the Laplace approximation to compute the likelihood function by integrating out all unknown system states. We make use of automatic differentiation in computing the posterior mode and in designing an efficient Metropolis--Hastings algorithm. We compare the new algorithm to the single-update Gibbs sampler and the integration sampler using a well-known time series of pound/dollar exchange rates. Copyright Royal Economic Society, 2003

Suggested Citation

  • Renate Meyer & David A. Fournier & Andreas Berg, 2003. "Stochastic volatility: Bayesian computation using automatic differentiation and the extended Kalman filter," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 408-420, December.
    • Handle: RePEc:ect:emjrnl:v:6:y:2003:i:2:p:408-420
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    Cited by:

    1. Jun Yu, 2007. "Automated Likelihood Based Inference for Stochastic Volatility Models," Working Papers 01-2007, Singapore Management University, Sim Kee Boon Institute for Financial Economics.
    2. Skaug, Hans J. & Yu, Jun, 2014. "A flexible and automated likelihood based framework for inference in stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 642-654.
    3. Tsyplakov, Alexander, 2010. "Revealing the arcane: an introduction to the art of stochastic volatility models," MPRA Paper 25511, University Library of Munich, Germany.
    4. Jun Yu & Renate Meyer, 2006. "Multivariate Stochastic Volatility Models: Bayesian Estimation and Model Comparison," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 361-384.
    5. Alexander Tsyplakov, 2010. "Revealing the arcane: an introduction to the art of stochastic volatility models (in Russian)," Quantile, Quantile, issue 8, pages 69-122, July.
    6. K. Triantafyllopoulos, 2008. "Multivariate stochastic volatility with Bayesian dynamic linear models," Papers 0802.0214, arXiv.org.
    7. Matthew Smith, 2012. "Estimating Nonlinear Economic Models Using Surrogate Transitions," 2012 Meeting Papers 494, Society for Economic Dynamics.
    8. Manabu Asai, 2005. "Comparison of MCMC Methods for Estimating Stochastic Volatility Models," Computational Economics, Springer;Society for Computational Economics, vol. 25(3), pages 281-301, June.
    9. Lee, Woojoo & Lim, Johan & Lee, Youngjo & del Castillo, Joan, 2011. "The hierarchical-likelihood approach to autoregressive stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 248-260, January.

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