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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. Nijman, T. & Sentana, E., 1993. "Marginalization and Contemporaneous Aggregation in Multivariate Garch Processes," Papers, Tilburg - Center for Economic Research 9312, Tilburg - Center for Economic Research.
  2. 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, Eastern Finance Association, vol. 37(2), pages 137-163, 05.
  3. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, Econometric Society, vol. 37(3), pages 424-38, July.
  4. Drost, F.C. & Nijman, T.E., 1992. "Temporal Aggregation of Garch Processes," Papers, Tilburg - Center for Economic Research 9240, Tilburg - Center for Economic Research.
  5. 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.
  6. Dufour, J.M. & Renault, E., 1995. "Short-Run and Long-Rub Causality in Time Series: Theory," Cahiers de recherche, Centre interuniversitaire de recherche en économie quantitative, CIREQ 9538, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  7. Cheung, Yin-Wong & Ng, Lilian K., 1996. "A causality-in-variance test and its application to financial market prices," Journal of Econometrics, Elsevier, Elsevier, vol. 72(1-2), pages 33-48.
  8. Granger, C. W. J., 1988. "Some recent development in a concept of causality," Journal of Econometrics, Elsevier, Elsevier, vol. 39(1-2), pages 199-211.
  9. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 84(1), pages 61-84, January.
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  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. 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.
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  14. 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., John Wiley & Sons, Ltd., vol. 7(3), pages 235-45, July.
  15. Pierce, David A. & Haugh, Larry D., 1977. "Causality in temporal systems : Characterization and a survey," Journal of Econometrics, Elsevier, Elsevier, vol. 5(3), pages 265-293, May.
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Citations

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Cited by:
  1. Matthieu Droumaguet & Tomasz Wozniak, 2012. "Bayesian Testing of Granger Causality in Markov-Switching VARs," Economics Working Papers, European University Institute ECO2012/06, European University Institute.
  2. Tomasz Wozniak, 2012. "Testing Causality Between Two Vectors in Multivariate GARCH Models," Department of Economics - Working Papers Series, The University of Melbourne 1139, The University of Melbourne.
  3. Hecq Alain & Laurent Sébastien & Palm Franz C., 2012. "On the Univariate Representation of BEKK Models with Common Factors," Research Memorandum 018, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  4. Gebka, Bartosz & Serwa, Dobromil, 2007. "Intra- and inter-regional spillovers between emerging capital markets around the world," Research in International Business and Finance, Elsevier, Elsevier, vol. 21(2), pages 203-221, June.
  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. Pablo Mendieta & Sergio Cerezo & Javier Cossio, 2009. "¿La inflación está de vuelta en Sudamérica?: choques exógenos, expectativas y credibilidad de la política monetaria," Monetaria, Centro de Estudios Monetarios Latinoamericanos, Centro de Estudios Monetarios Latinoamericanos, vol. 0(3), pages 359-389, octubre-d.
  7. Murat Tasdemir & Abdullah Yalama, 2010. "Inter-Regional Volatility Spillovers Between Emerging Capital Markets: Evidence From Turkey And Brazil," Working Papers, Turkish Economic Association 2010/8, Turkish Economic Association, revised Jan 2010.
  8. Grydaki, Maria & Bezemer, Dirk, 2013. "The role of credit in the Great Moderation: A multivariate GARCH approach," Journal of Banking & Finance, Elsevier, Elsevier, vol. 37(11), pages 4615-4626.
  9. 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, Banco de México 2009-10, Banco de México.
  10. Mario Reyna Cerecero & Diana Salazar Cavazos & Héctor Salgado Banda, 2009. "La curva de rendimiento y su relación con la actividad económica: una aplicación para México," Monetaria, Centro de Estudios Monetarios Latinoamericanos, Centro de Estudios Monetarios Latinoamericanos, vol. 0(3), pages 297-357, octubre-d.
  11. Tomasz Wozniak, 2012. "Granger-causal analysis of VARMA-GARCH models," Economics Working Papers, European University Institute ECO2012/19, European University Institute.
  12. Guillermo Benavides & Carlos Capistrán, 2009. "Una nota sobre las volatilidades de la tasa de interés y del tipo de cambio según diferentes instrumentos de política monetaria: México 1998-2008," Monetaria, Centro de Estudios Monetarios Latinoamericanos, Centro de Estudios Monetarios Latinoamericanos, vol. 0(3), pages 391-412, octubre-d.
  13. Javier Pereda, 2009. "Estimación de la curva de rendimiento para el Perú y su uso para el análisis monetario," Monetaria, Centro de Estudios Monetarios Latinoamericanos, Centro de Estudios Monetarios Latinoamericanos, vol. 0(3), pages 413-450, octubre-d.
  14. 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.

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