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Multivariate stochastic volatility with Bayesian dynamic linear models

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K. Triantafyllopoulos

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Abstract

This paper develops a Bayesian procedure for estimation and forecasting of the volatility of multivariate time series. The foundation of this work is the matrix-variate dynamic linear model, for the volatility of which we adopt a multiplicative stochastic evolution, using Wishart and singular multivariate beta distributions. A diagonal matrix of discount factors is employed in order to discount the variances element by element and therefore allowing a flexible and pragmatic variance modelling approach. Diagnostic tests and sequential model monitoring are discussed in some detail. The proposed estimation theory is applied to a four-dimensional time series, comprising spot prices of aluminium, copper, lead and zinc of the London metal exchange. The empirical findings suggest that the proposed Bayesian procedure can be effectively applied to financial data, overcoming many of the disadvantages of existing volatility models.

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File URL: http://arxiv.org/abs/0802.0214
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Publisher Info
Paper provided by arXiv.org in its series Quantitative Finance Papers with number 0802.0214.

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Date of creation: Feb 2008
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Publication status: Published in Journal of Statistical Planning and Inference (2008), 138(4), pp. 1021-1037
Handle: RePEc:arx:papers:0802.0214

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  1. Tse, Y K & Tsui, Albert K C, 2002. "A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model with Time-Varying Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 351-62, July.
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  3. Triantafyllopoulos, Kostas & Pikoulas, John, 2002. "Multivariate Bayesian Regression Applied to the Problem of Network Security," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 21(8), pages 579-94, December.
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  6. Jesús Crespo Cuaresma & Jaroslava Hlouskova, 2005. "Beating the random walk in Central and Eastern Europe," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 24(3), pages 189-201. [Downloadable!]
  7. 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. [Downloadable!] (restricted)
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  10. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2002. "Markov chain Monte Carlo methods for stochastic volatility models," Journal of Econometrics, Elsevier, vol. 108(2), pages 281-316, June. [Downloadable!] (restricted)
  11. Harald Uhlig, 1997. "Bayesian Vector Autoregressions with Stochastic Volatility," Econometrica, Econometric Society, vol. 65(1), pages 59-74, January.
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  12. Giovanni Barone-Adesi & Francesco Audrino, 2006. "Average conditional correlation and tree structures for multivariate GARCH models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(8), pages 579-600. [Downloadable!]
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  14. Michael D. McKenzie, Heather Mitchell, Robert D. Brooks, Robert W. Faff, 2001. "Power ARCH modelling of commodity futures data on the London Metal Exchange," European Journal of Finance, Taylor and Francis Journals, vol. 7(1), pages 22-38, March. [Downloadable!] (restricted)
    Other versions:
  15. Gita Persand & Chris Brooks, 2003. "Volatility forecasting for risk management," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 22(1), pages 1-22. [Downloadable!]
  16. James Chong, 2004. "Value at risk from econometric models and implied from currency options," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(8), pages 603-620. [Downloadable!]
  17. Kim, Sangjoon & Shephard, Neil & Chib, Siddhartha, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Blackwell Publishing, vol. 65(3), pages 361-93, July. [Downloadable!] (restricted)
    Other versions:
  18. Fiorentini, G. & Maravall, A., 1995. "Unobserved Components in ARCH Models: An Application to Seasonal Adjustment," Papers 9509, Centro de Estudios Monetarios Y Financieros-.
  19. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February. [Downloadable!]
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  20. Salvador, Manuel & Gargallo, Pilar, 2004. "Automatic monitoring and intervention in multivariate dynamic linear models," Computational Statistics & Data Analysis, Elsevier, vol. 47(3), pages 401-431, October. [Downloadable!] (restricted)
  21. Triantafyllopoulos, Kostas, 2006. "Multivariate discount weighted regression and local level models," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3702-3720, August. [Downloadable!] (restricted)
  22. Siddhartha Chib & Yasuhiro Omori & Manabu Asai, 2007. "Multivariate stochastic volatility," CIRJE F-Series CIRJE-F-488, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
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