Skip to main content
Article thumbnail
Location of Repository

Multivariate Stochastic Volatility Models: Bayesian Estimation and Model Comparison

By Jun Yu and Renate Meyer


In this paper we show that fully likelihood-based estimation and comparison of multivariate stochastic volatility (SV) models can be easily performed via a freely available Bayesian software called WinBUGS. Moreover, we introduce to the literature several new specifications which are natural extensions to certain existing models, one of which allows for time varying correlation coefficients. Ideas are illustrated by fitting, to a bivariate time series data of weekly exchange rates, nine multivariate SV models, including the specifications with Granger causality in volatility, time varying correlations, heavytailed error distributions, additive factor structure, and multiplicative factor structure. Empirical results suggest that the most adequate specifications are those that allow for time varying correlation coefficients.Multivariate stochastic volatility; Granger causality in volatility; Heavy-tailed distributions; Time varying correlations; Factors; MCMC; DIC.

OAI identifier:

Suggested articles


  1. (1998). A capital asset pricing model with time varying covariances.
  2. (1998). A maximum likelihood approach for non-Gaussian stochastic volatility models.
  3. (2002). A multivariate GARCH model with time-varying correlations.
  4. (2004). An Introduction to Modern Bayesian Econometrics.
  5. (2002). Analysis of high dimensional multivariate stochastic volatility models.
  6. (1994). Approximate Bayesian inferences by the weighted likelihood bootstrap.
  7. (1990). Asset pricing with a factor ARCH covariance structure: Empirical estimates for treasury bills.
  8. (1994). Bayesian analysis of stochastic volatility models.
  9. (2000). Bayesian dynamic fatcor models and portfolio allocation.
  10. (1996). BUGS 0.5, Bayesian inference using Gibbs sampling. Manual (version ii). MRC Biostatistics Unit,
  11. (2000). BUGS for a Bayesian analysis of stochastic volatility models.
  12. (2002). Correlated ARCH (CorrARCH): modelling the time-varying conditional correlation between fianacial asset returns.
  13. (1992). Derivative-free adaptive rejection sampling for Gibbs sampling.
  14. (2004). Deviance information criterion for comparing stochastic volatility models.
  15. (2002). Dynamic conditional correlation - A simple class of multivariate GARCH models.
  16. (2004). Efficient high-dimensional importance sampling. Working Paper,
  17. (1999). Efficient method of moments estimation of a stochastic volatility model: A Monte Carlo study.
  18. (2002). Estimation of the stochastic volatility model by the empirical characteristic function method.
  19. (2002). Forecasting volatility in the New Zealand stock market.
  20. (1990). Forecasting, Structural Time Series Models and the Kalman Filter.
  21. (2004). Free float and stochastic volatility: The experience of a small open economy.
  22. (1996). GMM estimation of a stochastic volatility model: A Monte Carlo study.
  23. (1995). Good news, bad news, volatility and betas.
  24. (1973). Information theory and an extension of the maximum likelihood principle.
  25. (2001). Large scale conditional covariance modelling, estimation and testing. Academia Economic Papers.
  26. (1995). Marginal likelihood from the Gibbs output.
  27. (1997). Markov Chain Monte Carlo methods based on ¸ Sslicingˇ T the density function.
  28. (1998). Maximum likelihood estimation of stochastic volatility models.
  29. (1990). Modelling the coherence in shirt-run nominal exchange rates: A multivariate generalized ARCH approach.
  30. (2004). Monte Carlo Methods for Estimating, Smoothing, and Filtering One and Two-Factor Stochastic Volatility Models.
  31. (1994). Multivariate stochastic variance models.
  32. (2004). Multivariate stochastic volatility models: A survey. Work in progress.
  33. (1998). Multivariate stochastic volatility models: Estimation and comparison with VGARCH models.
  34. (2003). Multivariate stochastic volatility with leverage.
  35. (2004). On leverage in a stochastic volatility model.
  36. (1990). Pricing foreign currency options with stochastic volatility.
  37. (1995). Priors and models of stochastic volatility models.
  38. (1994). Stochastic volatility in asset prices: Estimation with simulated maximum likelihood.
  39. (2003). Stochastic volatility: Bayesian computation using automatic differentiation and the extended Kalman filter.
  40. (1998). Stochastic volatility: Likelihood inference and comparison with ARCH models.
  41. (2004). Stochastic Volatility: Selected Readings.
  42. (1999). Stochastic volatility: Univariate and multivariate extensions.
  43. (1998). Suppressing random walks in Markov Chain Monte Carlo methods using ordered over-relaxation. In Learning in Graphical Models,( M . I .J o r d a n ,e d ) ,K l u w e r Academic Publishers,
  44. (1999). Time varying covariances: A factor stochastic volatility approach.
  45. (2003). Univariate and multivariate stochastic volatility models: estimation and diagnostics.

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.