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Testing for Causality in Variance using Multivariate GARCH Models

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  • Hafner, Christian M.
  • Herwartz, Helmut

Abstract

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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Bibliographic Info

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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Keywords: causality; multivariate volatility; local power;

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References

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  1. 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.
  2. 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.
  3. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-27, July.
  4. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  5. Nijman, T.E. & Sentana, E., 1996. "Marginalization and contemporaneous aggregation in multivariate GARCH processes," Open Access publications from Tilburg University urn:nbn:nl:ui:12-73202, Tilburg University.
  6. 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.
  7. 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.
  8. 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.
  9. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 61-84, January.
  10. 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.
  11. repec:wop:humbsf:1998-41 is not listed on IDEAS
  12. 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.
  13. Hafner, C.M. & Herwartz, H., 2003. "Analytical quasi maximum likelihood inference in multivariate volatility models," Econometric Institute Report EI 2003-21, Erasmus University Rotterdam, Econometric Institute.
  14. 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.
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Cited by:
  1. Matthieu Droumaguet & Tomasz Wozniak, 2012. "Bayesian Testing of Granger Causality in Markov-Switching VARs," Economics Working Papers ECO2012/06, European University Institute.
  2. Gebka, Bartosz & Serwa, Dobromil, 2007. "Intra- and inter-regional spillovers between emerging capital markets around the world," Research in International Business and Finance, Elsevier, vol. 21(2), pages 203-221, June.
  3. Hecq Alain & Laurent Sébastien & Palm Franz C., 2012. "On the Univariate Representation of BEKK Models with Common Factors," Research Memoranda 018, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization.
  4. Grydaki, Maria & Bezemer, Dirk J., 2012. "The Role of Credit in Great Moderation: a Multivariate GARCH Approach," MPRA Paper 39813, University Library of Munich, Germany.
  5. Bezemer, Dirk J & Grydaki, Maria, 2012. "Mortgage Lending and the Great moderation: a multivariate GARCH Approach," MPRA Paper 36356, University Library of Munich, Germany.
  6. Guillermo Benavides & Carlos Capistrán, 2009. "A Note on the Volatilities of the Interest Rate and the Exchange Rate Under Different Monetary Policy Instruments: Mexico 1998-2008," Working Papers 2009-10, Banco de México.

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