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Testing for causality in variance using multivariate GARCH models

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Author Info
Hafner, C.M.
Herwartz, H. (Erasmus Econometric Institute)

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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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File URL: http://hdl.handle.net/1765/1285
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Paper provided by Erasmus University Rotterdam, Econometric Institute in its series Econometric Institute Report with number EI 2004-20 Revision_Date: 2009-07-29.

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Date of creation: 21 May 2004
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Handle: RePEc:dgr:eureir:1765001285

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Keywords: causality; multivariate volatility; local power;

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References listed on IDEAS
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  1. Christian M. Hafner, 2003. "Fourth Moment Structure of Multivariate GARCH Models," Journal of Financial Econometrics, Oxford University Press, 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. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  4. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-27, July. [Downloadable!] (restricted)
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  5. 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. [Downloadable!] (restricted)
  6. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February. [Downloadable!]
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  7. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 61-84, January. [Downloadable!] (restricted)
  8. Christian Hafner & Helmut Herwartz, 2008. "Analytical quasi maximum likelihood inference in multivariate volatility models," Metrika, Springer, vol. 67(2), pages 219-239, March. [Downloadable!] (restricted)
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  9. 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.
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  10. H. Herwartz, . "Structural Analysis of Portfolio Risk Using Beta Impulse Response Functions," Sonderforschungsbereich 373 1998-41, Humboldt Universitaet Berlin.
  11. 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. [Downloadable!] (restricted)
  12. Nijman, Theo & Sentana, Enrique, 1996. "Marginalization and contemporaneous aggregation in multivariate GARCH processes," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 71-87. [Downloadable!] (restricted)
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