IDEAS home Printed from https://ideas.repec.org/p/arx/papers/0802.0214.html
   My bibliography  Save this paper

Multivariate stochastic volatility with Bayesian dynamic linear models

Author

Listed:
  • K. Triantafyllopoulos

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.

Suggested Citation

  • K. Triantafyllopoulos, 2008. "Multivariate stochastic volatility with Bayesian dynamic linear models," Papers 0802.0214, arXiv.org.
  • Handle: RePEc:arx:papers:0802.0214
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/0802.0214
    File Function: Latest version
    Download Restriction: no

    References listed on IDEAS

    as
    1. A. C. Harvey, 1986. "Analysis and Generalisation of a Multivariate Exponential Smoothing Model," Management Science, INFORMS, vol. 32(3), pages 374-380, March.
    2. Michael McKenzie & Heather Mitchell & Robert Brooks & Robert Faff, 2001. "Power ARCH modelling of commodity futures data on the London Metal Exchange," The European Journal of Finance, Taylor & Francis Journals, vol. 7(1), pages 22-38.
    3. Roman Liesenfeld & Jean-Francois Richard, 2006. "Classical and Bayesian Analysis of Univariate and Multivariate Stochastic Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 335-360.
    4. Gita Persand & Chris Brooks, 2003. "Volatility forecasting for risk management," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 22(1), pages 1-22.
    5. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility," Microeconomics Working Papers 22058, East Asian Bureau of Economic Research.
    6. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
    7. Esfandiar Maasoumi & Michael McAleer, 2006. "Multivariate Stochastic Volatility: An Overview," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 139-144.
    8. 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..
    9. Harvey, Andrew & Snyder, Ralph D., 1990. "Structural time series models in inventory control," International Journal of Forecasting, Elsevier, vol. 6(2), pages 187-198, July.
    10. 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.
    11. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 145-175.
    12. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
    13. repec:bla:restud:v:65:y:1998:i:3:p:361-93 is not listed on IDEAS
    14. 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 579-594, December.
    15. De Gooijer, Jan G. & Hyndman, Rob J., 2006. "25 years of time series forecasting," International Journal of Forecasting, Elsevier, vol. 22(3), pages 443-473.
    16. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    17. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 61-84, January.
    18. Philipov, Alexander & Glickman, Mark E., 2006. "Multivariate Stochastic Volatility via Wishart Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 313-328, July.
    19. Aguilar, Omar & West, Mike, 2000. "Bayesian Dynamic Factor Models and Portfolio Allocation," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 338-357, July.
    20. Renate Meyer & David A. Fournier & Andreas Berg, 2003. "Stochastic volatility: Bayesian computation using automatic differentiation and the extended Kalman filter," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 408-420, December.
    21. 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 135-152, Suppl. De.
    22. Alexander Philipov & Mark Glickman, 2006. "Factor Multivariate Stochastic Volatility via Wishart Processes," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 311-334.
    23. 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.
    24. Clinton Watkins & Michael McAleer, 2004. "Econometric modelling of non-ferrous metal prices," Journal of Economic Surveys, Wiley Blackwell, vol. 18(5), pages 651-701, December.
    25. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 247-264.
    26. Fiorentini, G. & Maravall, A., 1995. "Unobserved Components in ARCH Models: An Application to Seasonal Adjustment," Papers 9509, Centro de Estudios Monetarios Y Financieros-.
    27. 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.
    28. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    29. 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.
    30. 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.
    31. 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.
    32. Harald Uhlig, 1997. "Bayesian Vector Autoregressions with Stochastic Volatility," Econometrica, Econometric Society, vol. 65(1), pages 59-74, January.
    33. 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 351-362, July.
    34. 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.
    35. 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.
    36. Triantafyllopoulos, Kostas, 2006. "Multivariate discount weighted regression and local level models," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3702-3720, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. K. Triantafyllopoulos, 2012. "Multi‐variate stochastic volatility modelling using Wishart autoregressive processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(1), pages 48-60, January.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:0802.0214. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators). General contact details of provider: http://arxiv.org/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.