A Multivariate GARCH-M Model for Exchange Rates in the US, Germany and Japan

  • W. Polasek
  • L. Ren
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


After the so-called Asia crisis in the summer of 1997 the financial markets were shaken by increased volatility transmission around the world. Therefore, in this paper we will analyse the daily exchange rates in New York, Germany, and Japan for the period of 2 years (June 21, 1996 to June 22, 1998). We estimate a VAR-GARCH in mean model and estimate the multivariate volatility effects between the time series. We are also interested in the question of whether or not the volatility of the 3 exchange rates will feed back on the returns of the exchange rates. Using the marginal likelihood criterion for model selection we choose a VAR-GARCH-M (1,1,2,2) model. The model is estimated using MCMC methods and the coefficients show a quite rich transmission pattern between the financial markets. Comparing the predictive densities we see that the VAR-GARCH-M model produces forecasts with much smaller standard deviations.


Exchange Rate Marginal Likelihood Impulse Response Function Stochastic Volatility Model Predictive Density 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Aitkin, M. (1991): Posterior Bayes Factors. J.R.Statistical Soc. B, 1, 111–142.Google Scholar
  2. Chib, S. (1995): Marginal likelihood from the Gibbs output. JASA 90, 1313–1321.CrossRefGoogle Scholar
  3. Engle, R. F. (1995): ARCH, Selected Readings. Oxford University Press, Oxford.Google Scholar
  4. Engle, R. F., Lilien, D. M., and Robins, R. P. (1987): Estimating Time-Varying Risk Premia in the Term Structure, Econometrica 55/2 391-407, reprinted in Engle (1995) 24–41.Google Scholar
  5. Engle, R. F., Ito, T., and Lin, W. L. (1990): Meteor Showers or Heat Waves? Heteroskedastic Intra-Daily Volatility in the Foreign Exchange Market. Econometrica 58/3, 525–542.CrossRefGoogle Scholar
  6. Gelfand, A.E. and Smith, A.F.M. (1990): Sampling based approaches to calculating marginal densities. Journal of American Statistical Association, 85, 398–409.CrossRefGoogle Scholar
  7. Gelfand, A.E. and Dey, D.K. (1994): Bayesian model choice asymptotics and exact calculations. JRSSB, 56, 501–514Google Scholar
  8. Hamilton, J. (1994): Time Series Analysis, Princeton Univ. Press, New York.Google Scholar
  9. Liu, S. and Polasek, W. (1999): Maximum likelihood estimation based on the method of scoring for a vector autoregressive ARCH-M model. ISO-WWZ, University of Basel, mimeo.Google Scholar
  10. Pelloni, G. and Polasek, W. (1998): Intersectoral Labour Reallocation and Employment Volatility: A Bayesian analysis using a VAR-GARCH-M model. ISO-WWZ, University of Basel, mimeo.Google Scholar
  11. Polasek, W. Et Al. (1998): The BASEL package, ISO-WWZ, University of Basel. ( Scholar
  12. Polasek, W. (1999): Forecast evaluations for multiple time series: A generalized Theil decomposition. ISO-WWZ, University of Basel, mimeo. ( Scholar
  13. Polasek, W. and Ren, L. (1997): Structural breaks and model selection with marginal likelihoods. Proceedings of the Workshop on Model Selection, in: Racugno W. (ed.), Cagliari 223-274.Google Scholar
  14. Polasek, W. and Ren, L. (1999): Multivariate GARCH-M model for stock returns in the US, Germany and Japan. ISO-WWZ, University of Basel, mimeo.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • W. Polasek
    • 1
  • L. Ren
    • 1
  1. 1.Institute of Statistics and EconometricsUniversity of BaselSwitzerland

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