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Testing for Causality in Variance using Multivariate GARCH Models

  • Hafner, Christian M.
  • Herwartz, Helmut

Tests of causality in variance in multiple time series have been proposed recently, based on residuals of estimated univariate models. Although such tests are applied frequently little is known about their power properties. In this paper we show that a convenient alternative to residual based testing is to specify a multivariate volatility model, such as multivariate GARCH (or BEKK), and construct a Wald test on noncausality in variance. We compare both approaches to testing causality in variance in terms of asymptotic and finite sample properties. The Wald test is shown to have superior power properties under a sequence of local alternatives. Furthermore, we show by simulation that the Wald test is quite robust to misspecification of the order of the BEKK model, but that empirical power decreases substantially when asymmetries in volatility are ignored.

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Paper provided by Christian-Albrechts-University of Kiel, Department of Economics in its series Economics Working Papers with number 2004,03.

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Date of creation: 2004
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Handle: RePEc:zbw:cauewp:1690
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  1. Jean-Marie Dufour & Eric Renault, 1998. "Short Run and Long Run Causality in Time Series: Theory," Econometrica, Econometric Society, vol. 66(5), pages 1099-1126, September.
  2. Drost, F.C. & Nijman, T.E., 1992. "Temporal aggregation of GARCH processes," Discussion Paper 1992-40, Tilburg University, Center for Economic Research.
  3. Caporale, Guglielmo Maria & Pittis, Nikitas & Spagnolo, Nicola, 2002. "Testing for Causality-in-Variance: An Application to the East Asian Markets," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 7(3), pages 235-45, July.
  4. Hafner, C.M. & Herwartz, H., 2003. "Analytical quasi maximum likelihood inference in multivariate volatility models," Econometric Institute Research Papers EI 2003-21, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  5. Granger, C. W. J., 1988. "Some recent development in a concept of causality," Journal of Econometrics, Elsevier, vol. 39(1-2), pages 199-211.
  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. Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Other publications TiSEM 0642fb61-c7f4-4281-b484-4, School of Economics and Management.
  8. Granger, C. W. J., 1980. "Testing for causality : A personal viewpoint," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 329-352, May.
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  10. Nijman, T. & Sentana, E., 1993. "Marginalization and Contemporaneous Aggregation in Multivariate Garch Processes," Papers 9312, Tilburg - Center for Economic Research.
  11. Christian M. Hafner, 2003. "Fourth Moment Structure of Multivariate GARCH Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(1), pages 26-54.
  12. Angelos Kanas, 2002. "Mean and Variance Causality between Official and Parallel Currency Markets: Evidence from Four Latin American Countries," The Financial Review, Eastern Finance Association, vol. 37(2), pages 137-163, 05.
  13. Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report 157, Federal Reserve Bank of Minneapolis.
  14. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 61-84, January.
  15. H. Herwartz, 1998. "Structural Analysis of Portfolio Risk Using Beta Impulse Response Functions," SFB 373 Discussion Papers 1998,41, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  16. repec:ner:tilbur:urn:nbn:nl:ui:12-73202 is not listed on IDEAS
  17. Nijman, T.E. & Sentana, E., 1996. "Marginalization and contemporaneous aggregation in multivariate GARCH processes," Other publications TiSEM 1faf40e0-ce91-45fd-a98d-4, School of Economics and Management.
  18. Pierce, David A. & Haugh, Larry D., 1977. "Causality in temporal systems : Characterization and a survey," Journal of Econometrics, Elsevier, vol. 5(3), pages 265-293, May.
  19. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-38, July.
  20. 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.
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