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Temporal aggregation of multivariate GARCH processes

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  • Christian M. Hafner

Abstract

This paper derives results for the temporal aggregation of multivariate GARCH processes in the general vector specification. It is shown that the class of weak multivariate GARCH processes is closed under temporal aggregation. Fourth moment characteristics turn out to be crucial for the low frequency dynamics for both stock and flow variables. The framework used in this paper can easily be extended to investigate joint temporal and contemporaneous aggregation. Discussing causality in volatility, I find that there is not much room for spurious instantaneous causality in multivariate GARCH processes, but that spurious Granger causality will be more common however numerically insignificant. Forecasting volatility, it is generally advisable to aggregate forecasts of the disaggregate series rather than forecasting the aggregated series directly, and unlike for VARMA processes the advantage does not diminish for large forecast horizons. Finally, results are derived for the distribution of multivariate realized volatility if the high frequency process follows multivariate GARCH. A numerical example illustrates some of the results

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society 2004 North American Winter Meetings with number 538.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nawm04:538

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Keywords: multivariate GARCH; temporal aggregation; causality in volatility; forecasting volatility; realized volatility;

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References

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  1. Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153273, Tilburg University.
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  3. BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen VK, . "Multivariate GARCH models: a survey," CORE Discussion Papers RP -1847, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Nour Meddahi & Éric Renault, 2000. "Temporal Aggregation of Volatility Models," CIRANO Working Papers 2000s-22, CIRANO.
  5. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(01), pages 70-86, February.
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  7. Nijman, T. & Sentana, E., 1993. "Marginalization and Contemporaneous Aggregation in Multivariate Garch Processes," Papers 9312, Tilburg - Center for Economic Research.
  8. Eric Renault & Khalid Sekkat & Ariane Szafarz, 1998. "Testing for Spurious Causality in Exchange Rates," ULB Institutional Repository 2013/709, ULB -- Universite Libre de Bruxelles.
  9. 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.
  10. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  11. Christian M. Hafner, 2009. "Causality and forecasting in temporally aggregated multivariate GARCH processes," Econometrics Journal, Royal Economic Society, vol. 12(1), pages 127-146, 03.
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  15. Renault, E. & Szafarz, A., 1991. "True Versus Spurious Instantaneous Causality," Papers 9103, Universite Libre de Bruxelles - C.E.M.E..
  16. 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.
  17. Werker, B.J.M. & Drost, F.C., 1996. "Closing the GARCH gap: Continuous time GARCH modeling," Open Access publications from Tilburg University urn:nbn:nl:ui:12-72561, Tilburg University.
  18. Roy van der Weide, 2002. "GO-GARCH: a multivariate generalized orthogonal GARCH model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 549-564.
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Citations

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Cited by:
  1. Kourentzes, Nikolaos & Petropoulos, Fotios & Trapero, Juan R., 2014. "Improving forecasting by estimating time series structural components across multiple frequencies," International Journal of Forecasting, Elsevier, vol. 30(2), pages 291-302.
  2. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
  3. Andrea, SILVESTRINI, 2005. "Temporal aggregaton of univariate linear time series models," Discussion Papers (ECON - Département des Sciences Economiques) 2005044, Université catholique de Louvain, Département des Sciences Economiques.
  4. Peter Boswijk, H. & van der Weide, Roy, 2011. "Method of moments estimation of GO-GARCH models," Journal of Econometrics, Elsevier, vol. 163(1), pages 118-126, July.
  5. Sbrana, Giacomo & Poloni, Federico, 2013. "A closed-form estimator for the multivariate GARCH(1,1) model," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 152-162.

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