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Automated Likelihood Based Inference for Stochastic Volatility Models

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  • Hans J. Skaug

    ()
    (Department of Mathematics, University of Bergen)

  • Jun Yu

    ()
    (School of Economics, Singapore Management University)

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Abstract

In this paper the Laplace approximation is used to perform classical and Bayesian analyses of univariate and multivariate stochastic volatility (SV) models. We show that implementation of the Laplace approximation is greatly simplified by the use of a numerical technique known as automatic differentiation (AD). Several algorithms are proposed and compared withsome existing methods using both simulated data and actual data in terms of computational,statistical and simulation efficiency. It is found that the new methods match the statistical efficiency of the existing classical methods and substantially reduce the simulation inefficiency in some existing Bayesian Markov chain Monte Carlo (MCMC) algorithms. Also proposed are simple methods for obtaining the filtered, smoothed and forecasted latent variable. The new methods are implemented using the software AD Model Builder, which with its latent variable module (ADMB-RE) facilitates the formulation and fitting of SV models. To illustrate the flexibility of the new algorithms, several univariate and multivariate SV models are fitted using exchange rate data.

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Bibliographic Info

Paper provided by Singapore Management University, School of Economics in its series Working Papers with number 15-2009.

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Length: 27 pages
Date of creation: Nov 2009
Date of revision:
Publication status: Published in SMU Economics and Statistics Working Paper Series
Handle: RePEc:siu:wpaper:15-2009

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Keywords: Laplace approximation; Automatic differentiation; Simulated maximum likelihood; Importance sampling; Bayesian MCMC.;

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References

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Cited by:
  1. Peter C.B.Phillips & Jun Yu, . "Simulation-based Estimation of Contingent Claims Prices," Working Papers CoFie-05-2008, Sim Kee Boon Institute for Financial Economics.
  2. Yu, Jun, 2012. "A semiparametric stochastic volatility model," Journal of Econometrics, Elsevier, Elsevier, vol. 167(2), pages 473-482.
  3. Ola L{\o}vsletten & Martin Rypdal, 2012. "A multifractal approach towards inference in finance," Papers 1202.5376, arXiv.org.

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