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Stochastic Volatility: Likelihood Inference And Comparison With Arch Models

Author

Listed:
  • Sangjoon Kim

    (Salomon Brothers Asia Limited, Tokyo, Japan)

  • Neil Shephard

    (Nuffield College, Oxford University, Oxford)

  • Siddhartha Chib

    (Washington University, St. Louis)

Abstract

In this paper, Markov chain Monte Carlo sampling methods are exploited to provide a unified, practical likelihood-based framework for the analysis of stochastic volatility models. A highly effective method is developed that samples all the unobserved volatilities at once using an approximating offset mixture model, followed by an importance reweighting procedure. This approach is compared with several alternative methods using real data. The paper also develops simulation- based methods for filtering, likelihood evaluation and model failure diagnostics. The issue of model choice using non-nested likelihood ratios and Bayes factors is also investigated. These methods are used to compare the fit of stochastic volatility and GARCH models. All the procedures are illustrated in detail.

Suggested Citation

  • Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1996. "Stochastic Volatility: Likelihood Inference And Comparison With Arch Models," Econometrics 9610002, EconWPA.
  • Handle: RePEc:wpa:wuwpem:9610002 Note: Type of Document -
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    References listed on IDEAS

    as
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    Cited by:

    1. Diebold, Giorgianni, & Inoue, "undated". "Stamp 5.0: A Review," Home Pages _058, University of Pennsylvania.
    2. Salima El Kolei, 2013. "Parametric estimation of hidden stochastic model by contrast minimization and deconvolution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(8), pages 1031-1081, November.
    3. Pascale VALERY (HEC-Montreal) & Jean-Marie Dufour (University of Montreal), 2004. "A simple estimation method and finite-sample inference for a stochastic volatility model," Econometric Society 2004 North American Summer Meetings 153, Econometric Society.
    4. Jiang, George J., 1998. "Jump-diffusion model of exchange rate dynamics : estimation via indirect inference," Research Report 98A40, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    5. Lombardi, Marco J. & Calzolari, Giorgio, 2009. "Indirect estimation of [alpha]-stable stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2298-2308, April.
    6. Roman Liesenfeld & Robert C. Jung, 2000. "Stochastic volatility models: conditional normality versus heavy-tailed distributions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(2), pages 137-160.
    7. Font, Begoña, 1998. "Modelización de series temporales financieras. Una recopilación," DES - Documentos de Trabajo. Estadística y Econometría. DS 3664, Universidad Carlos III de Madrid. Departamento de Estadística.
    8. Danielsson, Jon, 1998. "Multivariate stochastic volatility models: Estimation and a comparison with VGARCH models," Journal of Empirical Finance, Elsevier, vol. 5(2), pages 155-173, June.
    9. Francis X. Diebold & Jose A. Lopez, 1995. "Measuring Volatility Dynamics," NBER Technical Working Papers 0173, National Bureau of Economic Research, Inc.
    10. Dwyer, Gerald Jr. & Williams, K. B., 2003. "Portable random number generators," Journal of Economic Dynamics and Control, Elsevier, vol. 27(4), pages 645-650, February.
    11. Ming Liu & Harold H. Zhang, "undated". "Specification Tests in the Efficient Method of Moments Framework with Application to the Stochastic Volatility Models," Computing in Economics and Finance 1997 93, Society for Computational Economics.
    12. G Sandmann & Siem Jan Koopman, 1996. "Maximum Likelihood Estimation of Stochastic Volatility Models," FMG Discussion Papers dp248, Financial Markets Group.
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    14. Kondo, Koji, 1997. "Statistical analysis of foreign exchange rates: application of cointegration model and regime-switching stochastic volatility model," ISU General Staff Papers 1997010108000012997, Iowa State University, Department of Economics.
    15. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
    16. Koehler, Anne & Diebold, Francis X. & Giogianni, Lorenzo & Inoue, Atsushi, 1996. "Software review," International Journal of Forecasting, Elsevier, vol. 12(2), pages 309-315, June.

    More about this item

    Keywords

    Bayes estimation; Bayes factors; GARCH; Gibbs sampler; Heteroscedasticity; Maximum~likelihood; Likelihood ratio; Markov chain Monte Carlo; Quasi-maximum likelihood; Simulation; Stochastic EM algorithm; Stochastic volatility; Stock returns.;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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