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Automated Likelihood Based Inference for Stochastic Volatility Models

Author

Listed:
  • Hans J. Skaug

    () (Department of Mathematics, University of Bergen)

  • Jun Yu

    () (School of Economics, Singapore Management University)

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.

Suggested Citation

  • Hans J. Skaug & Jun Yu, 2009. "Automated Likelihood Based Inference for Stochastic Volatility Models," Working Papers 15-2009, Singapore Management University, School of Economics.
  • Handle: RePEc:siu:wpaper:15-2009
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    File URL: https://mercury.smu.edu.sg/rsrchpubupload/15724/sml_ADMB13.pdf
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    References listed on IDEAS

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    Cited by:

    1. Ola L{o}vsletten & Martin Rypdal, 2012. "A multifractal approach towards inference in finance," Papers 1202.5376, arXiv.org.

    More about this item

    Keywords

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

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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