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Multivariate Stochastic Volatility Models: Bayesian Estimation and Model Comparison

Author

Listed:
  • Jun Yu
  • Renate Meyer

Abstract

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 that 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, heavy-tailed error distributions, additive factor structure, and multiplicative factor structure. Empirical results suggest that the best specifications are those that allow for time-varying correlation coefficients.

Suggested Citation

  • Jun Yu & Renate Meyer, 2006. "Multivariate Stochastic Volatility Models: Bayesian Estimation and Model Comparison," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 361-384.
  • Handle: RePEc:taf:emetrv:v:25:y:2006:i:2-3:p:361-384
    DOI: 10.1080/07474930600713465
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    References listed on IDEAS

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    1. Eric Jacquier & Nicholas G. Polson & Peter Rossi, "undated". "Stochastic Volatility: Univariate and Multivariate Extensions," Rodney L. White Center for Financial Research Working Papers 19-95, Wharton School Rodney L. White Center for Financial Research.
    2. John L. Knight & Stephen E. Satchell & Jun Yu, 2002. "Estimation of the Stochastic Volatility Model by the Empirical Characteristic Function Method," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 44(3), pages 319-335, September.
    3. Andersen, Torben G & Sorensen, Bent E, 1996. "GMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 328-352, July.
    4. 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.
    5. Danielsson, Jon, 1994. "Stochastic volatility in asset prices estimation with simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 375-400.
    6. Friedman, Moshe & Harris, Lawrence, 1998. "A Maximum Likelihood Approach for Non-Gaussian Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 284-291, July.
    7. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
    8. Harvey,Andrew C., 1991. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521405737.
    9. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 247-264.
    10. Liesenfeld, Roman & Richard, Jean-Francois, 2003. "Univariate and multivariate stochastic volatility models: estimation and diagnostics," Journal of Empirical Finance, Elsevier, vol. 10(4), pages 505-531, September.
    11. Engle, Robert F. & Ng, Victor K. & Rothschild, Michael, 1990. "Asset pricing with a factor-arch covariance structure : Empirical estimates for treasury bills," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 213-237.
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    13. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August.
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    More about this item

    Keywords

    DIC; Factors; Granger causality in volatility; Heavy-tailed distributions; MCMC; Multivariate stochastic volatility; Time-varying correlations;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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