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Volatility impulse response functions for multivariate GARCH models

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  • HAFNER, Christian
  • HERWARTZ, Helmut

Abstract

In the empirical analysis of financial time series, multivariate GARCH models have been used in various forms. As it is typical for nonlinear models there is yet no unique framework available to uncover dynamic covariance relationships for vector return processes. We introduce a new concept of impulse response functions tracing the effects of independent shocks on volatility through time. The advocated methodology avoids typical orthogonalization and ordering problems. Theoretical properties of volatility impulse response functions are derived and compared with conditional moment profiles introduced by Gallant, Rossi and Tauchen (1993) for semi-nonparametric models. In an empirical study of a bivariate foreign exchange rate series we use volatility impulse response functions to compare alternative parametric volatility specifications. It is shown that for shocks affecting foreign exchange rates in an asymmetric way, the difference between our methodology and conditional volatility profiles can be substantial.

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2001039.

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Date of creation: 00 Sep 2001
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Handle: RePEc:cor:louvco:2001039

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Keywords: Multivariate GARCH; impulse response; exchange rate; volatility;

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References

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  1. Engle, Robert F & Ng, Victor K, 1993. " Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-78, December.
  2. Bollerslev, Tim & Engle, Robert F, 1993. "Common Persistence in Conditional Variances," Econometrica, Econometric Society, vol. 61(1), pages 167-86, January.
  3. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
  4. Drost, F.C. & Nijman, T.E., 1992. "Temporal Aggregation of Garch Processes," Papers 9240, Tilburg - Center for Economic Research.
  5. Rose, A.K. & Svensson, L.E.O., 1993. "European Exchange Rate Credibility Before the Fall," Papers 542, Stockholm - International Economic Studies.
  6. Koop, Gary & Pesaran, M. Hashem & Potter, Simon M., 1996. "Impulse response analysis in nonlinear multivariate models," Journal of Econometrics, Elsevier, vol. 74(1), pages 119-147, September.
  7. Hafner, Christian M. & Herwartz, Helmut, 1998. "Testing for linear autoregressive dynamics under heteroskedasticity," SFB 373 Discussion Papers 1999,7, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  8. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  9. Lin, Wen-Ling, 1997. "Impulse Response Function for Conditional Volatility in GARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 15-25, January.
  10. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
  11. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  12. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
  13. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1993. "Nonlinear Dynamic Structures," Econometrica, Econometric Society, vol. 61(4), pages 871-907, July.
  14. Bauwens, L. & Lubrano, M., 1997. "Bayesian Option Pricing Using Asymmetric GARCH," G.R.E.Q.A.M. 97a40, Universite Aix-Marseille III.
  15. John Freebairn & Bill Griffiths, 2006. "Introduction," The Economic Record, The Economic Society of Australia, vol. 82(s1), pages S1-S1, 09.
  16. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-31, February.
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Citations

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Cited by:
  1. Luis Fernando Melo Velandia & Oscar Reinaldo Becerra Camargo, . "Una aproximación a la dinámica de las tasas de interés de corto plazo en Colombia a través de modelos GARCH multivariados," Borradores de Economia 366, Banco de la Republica de Colombia.
  2. Hafner, C.M. & Rombouts, J.V.K., 2004. "Semiparametric multivariate volatility models," Econometric Institute Research Papers EI 2004-21, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  3. HAFNER, Christian, 2001. "Fourth moments of multivariate GARCH processes," CORE Discussion Papers 2001046, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. E.Panopoulou & T. Pantelidis, 2005. "Integration at a cost: Evidence from volatility impulse response functions," Economics, Finance and Accounting Department Working Paper Series n1540305, Department of Economics, Finance and Accounting, National University of Ireland - Maynooth.
  5. Kalvinder Shields & Nilss Olekalns & Ólan T. Henry & Chris Brooks, 2003. "Measuring the Response of Macroeconomic Uncertainty to Shocks," Department of Economics - Working Papers Series 870, The University of Melbourne.
  6. Olan T. Henry & Nilss Olekalns & Kalvinder Shields, 2004. "Time Variation And Asymmetry In The World Price Of Covariance Risk: The Implications For International Diversification," Department of Economics - Working Papers Series 907, The University of Melbourne.
  7. Walid Ben Omrane & Christian M. Hafner, 2009. "Information Spillover, Volatility and the Currency Markets for the Binary Choice Model," International Econometric Review (IER), Econometric Research Association, vol. 1(1), pages 50-62, April.

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