IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

Testing Causality Between Two Vectors in Multivariate GARCH Models

Listed author(s):
  • Tomasz Wozniak

Spillover and contagion effects have gained significant interest in the recent years of financial crisis. Attention has not only been directed to relations between returns of financial variables, but to spillovers in risk as well. I use the family of Constant Conditional Correlation GARCH models to model the risk associated with financial time series and to make inferences about Granger causal relations between second conditional moments. The restrictions for second-order Granger noncausality between two vectors of variables are derived. To assess the credibility of the noncausality hypotheses, I employ posterior odds ratios. This Bayesian method constitutes an alternative for classical tests that makes such testing possible, regardless of the form of the restrictions on the parameters of the model. Moreover, it relaxes the assumptions about the existence of higher-order moments of the processes required in classical tests. In the empirical example, I find that the pound-to-Euro exchange rate second-order causes the US dollar-to-Euro exchange rate, which confirms the meteor shower hypothesis of Engle, Ito & Lin (1990).

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
File Function: main text
Download Restriction: no

Paper provided by European University Institute in its series Economics Working Papers with number ECO2012/20.

in new window

Date of creation: 2012
Handle: RePEc:eui:euiwps:eco2012/20
Contact details of provider: Postal:
Badia Fiesolana, Via dei Roccettini, 9, 50014 San Domenico di Fiesole (FI) Italy

Phone: +39-055-4685.982
Fax: +39-055-4685.902
Web page:

More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

in new window

  1. Shiqing Ling & Michael McAleer, 2001. "Asymptotic Theory for a Vector ARMA-GARCH Model," ISER Discussion Paper 0549, Institute of Social and Economic Research, Osaka University.
  2. Christian Hafner & Helmut Herwartz, 2008. "Analytical quasi maximum likelihood inference in multivariate volatility models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(2), pages 219-239, March.
  3. John Geweke, 1999. "Using simulation methods for bayesian econometric models: inference, development,and communication," Econometric Reviews, Taylor & Francis Journals, vol. 18(1), pages 1-73.
  4. Hoogerheide, L.F. & van Dijk, H.K. & van Oest, R.D., 2007. "Simulation based bayesian econometric inference: principles and some recent computational advances," Econometric Institute Research Papers EI 2007-03, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  5. Hafner, Christian M. & Preminger, Arie, 2009. "Asymptotic Theory For A Factor Garch Model," Econometric Theory, Cambridge University Press, vol. 25(02), pages 336-363, April.
  6. Bénédicte Vidaillet & V. D'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL.
  7. Boudjellaba, H. & Dufour, J.M. & Roy, R., 1992. "Simplified Conditions for Non-Causality Between Vectors in Multivariate Arma Models," Cahiers de recherche 9236, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  8. Kim, Tae-Hwan & White, Halbert, 2004. "On more robust estimation of skewness and kurtosis," Finance Research Letters, Elsevier, vol. 1(1), pages 56-73, March.
  9. 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.
  10. Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
  11. Karolyi, G Andrew, 1995. "A Multivariate GARCH Model of International Transmissions of Stock Returns and Volatility: The Case of the United States and Canada," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 11-25, January.
  12. Tomasz Wozniak, 2012. "Granger-causal analysis of VARMA-GARCH models," Economics Working Papers ECO2012/19, European University Institute.
  13. Hafner, Christian M. & Herwartz, Helmut, 2006. "A Lagrange multiplier test for causality in variance," Economics Letters, Elsevier, vol. 93(1), pages 137-141, October.
  14. Deschamps, Philippe J., 2004. "A flexible prior distribution for Markov switching autoregressions with Student-t errors," DQE Working Papers 2, Department of Quantitative Economics, University of Freiburg/Fribourg Switzerland, revised 12 Nov 2011.
  15. Nakatani, Tomoaki & Teräsvirta, Timo, 2007. "Testing for Volatility Interactions in the Constant Conditional Correlation GARCH Model," SSE/EFI Working Paper Series in Economics and Finance 649, Stockholm School of Economics, revised 24 Jan 2007.
  16. Luc Bauwens & Michel Lubrano, 1998. "Bayesian inference on GARCH models using the Gibbs sampler," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages 23-46.
  17. Jean-Marie Dufour & David Tessier, 2006. "Short-Run and Long-Run Causality between Monetary Policy Variables and Stock Prices," Staff Working Papers 06-39, Bank of Canada.
  18. Conrad, Christian & Karanasos, Menelaos, 2010. "Negative Volatility Spillovers In The Unrestricted Eccc-Garch Model," Econometric Theory, Cambridge University Press, vol. 26(03), pages 838-862, June.
  19. Osiewalski, Jacek & Pipien, Mateusz, 2004. "Bayesian comparison of bivariate ARCH-type models for the main exchange rates in Poland," Journal of Econometrics, Elsevier, vol. 123(2), pages 371-391, December.
  20. Engle, Robert F & Ito, Takatoshi & Lin, Wen-Ling, 1990. "Meteor Showers or Heat Waves? Heteroskedastic Intra-daily Volatility in the Foreign Exchange Market," Econometrica, Econometric Society, vol. 58(3), pages 525-542, May.
  21. Fiorentini, Gabriele & Sentana, Enrique & Calzolari, Giorgio, 2003. "Maximum Likelihood Estimation and Inference in Multivariate Conditionally Heteroscedastic Dynamic Regression Models with Student t Innovations," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 532-546, October.
  22. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
  23. Jarociński, Marek & Maćkowiak, Bartosz, 2013. "Granger-causal-priority and choice of variables in vector autoregressions," Working Paper Series 1600, European Central Bank.
  24. Jean-Marie Dufour & Denis Pelletier & Éric Renault, 2003. "Short Run and Long Run Causality in Time Series: Inference," CIRANO Working Papers 2003s-61, CIRANO.
  25. Boudjellaba, B. & Dufour, J.M. & Roy, R., 1991. "Testing Causality Between Two Vectors in Multivariate Arma Models," Cahiers de recherche 9119, Universite de Montreal, Departement de sciences economiques.
  26. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
  27. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
  28. He, Changli & Ter svirta, Timo, 2004. "An Extended Constant Conditional Correlation Garch Model And Its Fourth-Moment Structure," Econometric Theory, Cambridge University Press, vol. 20(05), pages 904-926, October.
  29. Hafner, C.M. & Herwartz, H., 2004. "Testing for causality in variance using multivariate GARCH models," Econometric Institute Research Papers EI 2004-20, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  30. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
  31. Anna Pajor, 2011. "A Bayesian Analysis of Exogeneity in Models with Latent Variables," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 3(2), pages 49-73, June.
  32. Matthieu Droumaguet & Tomasz Wozniak, 2012. "Bayesian Testing of Granger Causality in Markov-Switching VARs," Economics Working Papers ECO2012/06, European University Institute.
  33. Dufour, J.M. & Renault, E., 1995. "Short-Run and Long-Rub Causality in Time Series: Theory," Cahiers de recherche 9538, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  34. Tatiana Miazhynskaia & Georg Dorffner, 2006. "A comparison of Bayesian model selection based on MCMC with an application to GARCH-type models," Statistical Papers, Springer, vol. 47(4), pages 525-549, October.
  35. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
  36. Sylvia Fruhwirth-Schnatter, 2004. "Estimating marginal likelihoods for mixture and Markov switching models using bridge sampling techniques," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 143-167, 06.
  37. Florens, J P & Mouchart, M, 1982. "A Note on Noncausality," Econometrica, Econometric Society, vol. 50(3), pages 583-591, May.
  38. Cheung, Yin-Wong & Ng, Lilian K., 1996. "A causality-in-variance test and its application to financial market prices," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 33-48.
  39. Florens, Jean-Pierre & Mouchart, Michel, 1985. "A Linear Theory for Noncausality," Econometrica, Econometric Society, vol. 53(1), pages 157-175, January.
  40. Sims, Christopher A, 1972. "Money, Income, and Causality," American Economic Review, American Economic Association, vol. 62(4), pages 540-552, September.
  41. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 61-84, January.
  42. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(01), pages 70-86, February.
  43. 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.
  44. Lutkepohl, Helmut & Burda, Maike M., 1997. "Modified Wald tests under nonregular conditions," Journal of Econometrics, Elsevier, vol. 78(2), pages 315-332, June.
  45. Z. Lomnicki, 1961. "Tests for departure from normality in the case of linear stochastic processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 4(1), pages 37-62, December.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:eui:euiwps:eco2012/20. 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: (Anne Banks)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.