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Efficient Estimation of a Multivariate Multiplicative Volatility Model

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  • Christian M. Hafner
  • Oliver Linton

Abstract

We propose a multivariate generalization of the multiplicative volatility model ofEngle and Rangel (2008), which has a nonparametric long run component and aunit multivariate GARCH short run dynamic component. We suggest variouskernel-based estimation procedures for the parametric and nonparametriccomponents, and derive the asymptotic properties thereof. For the parametric partof the model, we obtain the semiparametric efficiency bound. Our method isapplied to a bivariate stock index series. We find that the univariate model of Engleand Rangel (2008) appears to be violated in the data whereas our multivariatemodel is more consistent with the data.

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Bibliographic Info

Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2009/541.

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Date of creation: Oct 2009
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Handle: RePEc:cep:stiecm:/2009/541

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Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

Related research

Keywords: GARCH; Kernel Estimation; Local Stationarity; Semiparametric;

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References

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  1. Engle, Robert F & Sheppard, Kevin K, 2001. "Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH," University of California at San Diego, Economics Working Paper Series qt5s2218dp, Department of Economics, UC San Diego.
  2. Allan Timmermann & M. Hashem Pesaran, 2003. "How Costly is it to Ignore Breaks when Forecasting the Direction of a Time Series?," CESifo Working Paper Series 875, CESifo Group Munich.
  3. Catalin Starica, 2004. "Is GARCH(1,1) as good a model as the Nobel prize accolades would imply?," Econometrics 0411015, EconWPA.
  4. Boswijk, H.P. & Weide, R. van der, 2006. "Wake me up before you GO-GARCH," CeNDEF Working Papers 06-13, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  5. José Gonzalo Rangel & Robert F. Engle, 2012. "The Factor--Spline--GARCH Model for High and Low Frequency Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 30(1), pages 109-124, January.
  6. Lanne, Markku & Saikkonen, Pentti, 2007. "A Multivariate Generalized Orthogonal Factor GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 61-75, January.
  7. BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen, 2003. "Multivariate GARCH models: a survey," CORE Discussion Papers 2003031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. Lorenzo Cappiello & Robert F. Engle & Kevin Sheppard, 2006. "Asymmetric Dynamics in the Correlations of Global Equity and Bond Returns," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(4), pages 537-572.
  9. Jondeau, Eric & Rockinger, Michael, 2006. "The Copula-GARCH model of conditional dependencies: An international stock market application," Journal of International Money and Finance, Elsevier, vol. 25(5), pages 827-853, August.
  10. Andrew J. Patton, 2006. "Estimation of multivariate models for time series of possibly different lengths," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(2), pages 147-173.
  11. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 61-84, January.
  12. Pelletier, Denis, 2006. "Regime switching for dynamic correlations," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 445-473.
  13. H. Peter Boswijk & Roy van der Weide, 2006. "Wake me up before you GO-GARCH," Tinbergen Institute Discussion Papers 06-079/4, Tinbergen Institute, revised 21 Sep 2006.
  14. Andrew Patton, 2004. "Modelling Asymmetric Exchange Rate Dependence," Working Papers wp04-04, Warwick Business School, Financial Econometrics Research Centre.
  15. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  16. Kawakatsu, Hiroyuki, 2006. "Matrix exponential GARCH," Journal of Econometrics, Elsevier, vol. 134(1), pages 95-128, September.
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Citations

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Cited by:
  1. Luc Bauwens & Christian M. Hafner & Diane Pierret, 2011. "Multivariate Volatility Modeling of Electricity Futures," SFB 649 Discussion Papers SFB649DP2011-063, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  2. VAN BELLEGEM, Sébastien, 2011. "Locally stationary volatility modelling," CORE Discussion Papers 2011041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. repec:eca:wpaper:2013/57645 is not listed on IDEAS
  4. Michael Vogt, 2012. "Nonparametric regression for locally stationary time series," CeMMAP working papers CWP22/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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