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Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models

  • Kim, Sangjoon
  • Shephard, Neil
  • Chib, Siddhartha

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 nonnested 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. Copyright 1998 by The Review of Economic Studies Limited.

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Article provided by Wiley Blackwell in its journal Review of Economic Studies.

Volume (Year): 65 (1998)
Issue (Month): 3 (July)
Pages: 361-93

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Handle: RePEc:bla:restud:v:65:y:1998:i:3:p:361-93
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  1. Mervyn King & Enrique Sentana & Sushil Wadhwani, 1990. "Volatiltiy and Links Between National Stock Markets," NBER Working Papers 3357, National Bureau of Economic Research, Inc.
  2. Siddhartha Chib & Edward Greenberg, 1994. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometrics 9408001, EconWPA, revised 24 Oct 1994.
  3. Diebold, Francis X & Nerlove, Marc, 1989. "The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor Arch Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(1), pages 1-21, Jan.-Mar..
  4. Shephard, Neil, 1993. "Fitting Nonlinear Time-Series Models with Applications to Stochastic Variance Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S135-52, Suppl. De.
  5. Chib, Siddhartha & Greenberg, Edward, 1994. "Bayes inference in regression models with ARMA (p, q) errors," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 183-206.
  6. Neil Shephard, 2005. "Stochastic volatility," Economics Series Working Papers 2005-W17, University of Oxford, Department of Economics.
  7. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
  8. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  9. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(04), pages 657-681, October.
  10. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  11. Gourieroux, C. & Monfort, A. & Renault, E., 1992. "Indirect Inference," Papers 92.279, Toulouse - GREMAQ.
  12. Michael K Pitt & Neil Shephard, 1996. "Analytic convergence rates and parameterisation issues for the Gibbs sampler applied to state space models," Economics Papers 20 & 113, Economics Group, Nuffield College, University of Oxford.
  13. Neil Shephard & Michael K Pitt, 1995. "Likelihood analysis of non-Gaussian parameter driven models," Economics Papers 15 & 108., Economics Group, Nuffield College, University of Oxford.
  14. Phillips, P C B, 1991. "To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 333-64, Oct.-Dec..
  15. Gourieroux, C. & Monfort, A., 1986. "Testing non-nested hypotheses," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 44, pages 2583-2637 Elsevier.
  16. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August.
  17. Hashem Pesaran, M. & Pesaran, Bahram, 1993. "A simulation approach to the problem of computing Cox's statistic for testing nonnested models," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 377-392.
  18. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  19. Chesney, Marc & Scott, Louis, 1989. "Pricing European Currency Options: A Comparison of the Modified Black-Scholes Model and a Random Variance Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(03), pages 267-284, September.
  20. Michael K Pitt & Neil Shephard, . "Filtering via simulation: auxiliary particle filters," Economics Papers 1997-W13, Economics Group, Nuffield College, University of Oxford.
  21. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038 Elsevier.
  22. Ronald Mahieu & Peter Schotman, 1994. "Stochastic volatility and the distribution of exchange rate news," Discussion Paper / Institute for Empirical Macroeconomics 96, Federal Reserve Bank of Minneapolis.
  23. repec:cup:etheor:v:12:y:1996:i:3:p:409-31 is not listed on IDEAS
  24. Schotman, Peter & van Dijk, Herman K., 1991. "A Bayesian analysis of the unit root in real exchange rates," Journal of Econometrics, Elsevier, vol. 49(1-2), pages 195-238.
  25. A. W. Coats, 1996. "Introduction," History of Political Economy, Duke University Press, vol. 28(5), pages 3-11, Supplemen.
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  27. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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