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Automated Likelihood Based Inference for Stochastic Volatility Models

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  • Jun Yu

    (Sim Kee Boon Institute for Financial 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 with some 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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File URL: http://www.smu.edu.sg/institutes/skbife/downloads/CoFiE/Working%20Papers/Automated%20Likelihood%20Based%20Inference%20for%20Stochastic%20Volatility%20Models.pdf
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Bibliographic Info

Paper provided by Sim Kee Boon Institute for Financial Economics in its series Working Papers with number 01-2007.

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Length: 32 Pages
Date of creation: Nov 2007
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Publication status: Published in SMU-SKBI CoFie Working Paper
Handle: RePEc:skb:wpaper:01-2007

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

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  1. Jun Yu, 2004. "On Leverage in a Stochastic Volatility Model," Econometric Society 2004 Far Eastern Meetings 506, Econometric Society.
  2. Harvey, Andrew C & Shephard, Neil, 1996. "Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 429-34, October.
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  6. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 145-175.
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  27. Durbin, J. & Koopman, S.J.M., 1998. "Time Series Analysis of Non-Gaussian Observations Based on State Space Models from Both Classical and Bayesian Perspectives," Discussion Paper 1998-142, Tilburg University, Center for Economic Research.
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Citations

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Cited by:
  1. Peter C. B. Phillips & Jun Yu, 2008. "Simulation-based Estimation of Contingent-claims Prices," Finance Working Papers 22473, East Asian Bureau of Economic Research.
  2. Yu, Jun, 2012. "A semiparametric stochastic volatility model," Journal of Econometrics, 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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