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Stochastic volatility: likelihood inference and comparison with ARCH models

  • Sangjoon Kim, Neil Shephard
  • Siddhartha Chib

Stochastic volatility models present a natural way of working with time-varying volatility. However the difficulty involved in estimating these types of models has prevented their wide-spread use in empirical applications. In this paper we exploit Gibbs sampling to provide a likelihood framework for the analysis of stochastic volatility models, demonstrating how to perform either maximum likelihood or Bayesian estimation. The paper includes an extensive Monte Carlo experiment which compares the efficiency of the maximum likelihood estimator with that of quasi-likelihood and Bayesian estimators proposed in the literature. We also compare the fit of the stochastic volatility model to that of ARCH models using the likelihood criterion to illustrate the flexibility of the framework presented.

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Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number W26, revised version of W3.

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Handle: RePEc:nuf:econwp:9626
Contact details of provider: Web page: http://www.nuff.ox.ac.uk/economics/

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  1. Shephard, N. & Pitt, M.K., 1995. "Likelihood Analysis of Non-Gaussian Parameter-Driven Models," Economics Papers 108, Economics Group, Nuffield College, University of Oxford.
  2. 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.
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  4. 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..
  5. 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.
  6. 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.
  7. 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.
  8. Chib, Siddhartha & Greenberg, Edward, 1996. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometric Theory, Cambridge University Press, vol. 12(03), pages 409-431, August.
  9. 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.
  10. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  11. Tauchen, George E. & Gallant, A. Ronald, 1995. "Which Moments to Match," Working Papers 95-20, Duke University, Department of Economics.
  12. repec:cup:etheor:v:12:y:1996:i:3:p:409-31 is not listed on IDEAS
  13. 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.
  14. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  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. 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.
  17. 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.
  18. A. W. Coats, 1996. "Introduction," History of Political Economy, Duke University Press, vol. 28(5), pages 3-11, Supplemen.
  19. 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..
  20. 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.
  21. 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.
  22. King, Mervyn & Sentana, Enrique & Wadhwani, Sushil, 1994. "Volatility and Links between National Stock Markets," Econometrica, Econometric Society, vol. 62(4), pages 901-33, July.
  23. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Universite de Montreal, Departement de sciences economiques.
  24. 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.
  25. Michael K Pitt & Neil Shephard, . "Filtering via simulation: auxiliary particle filters," Economics Papers 1997-W13, Economics Group, Nuffield College, University of Oxford.
  26. Gourieroux, C. & Monfort, A. & Renault, E., 1992. "Indirect Inference," Papers 92.279, Toulouse - GREMAQ.
  27. 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.
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