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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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  1. 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.
  2. Robert F. Engle & Kevin Sheppard, 2001. "Theoretical and Empirical properties of Dynamic Conditional Correlation Multivariate GARCH," NBER Working Papers 8554, National Bureau of Economic Research, Inc.
  3. Andrew Patton, 2004. "Modelling Asymmetric Exchange Rate Dependence," Working Papers wp04-04, Warwick Business School, Finance Group.
  4. Denis Pelletier, 2004. "Regime Switching for Dynamic Correlations," Econometric Society 2004 North American Summer Meetings 230, Econometric Society.
  5. Sheppard, Kevin & Cappiello, Lorenzo & Engle, Robert F., 2003. "Asymmetric dynamics in the correlations of global equity and bond returns," Working Paper Series 0204, European Central Bank.
  6. Kawakatsu, Hiroyuki, 2006. "Matrix exponential GARCH," Journal of Econometrics, Elsevier, vol. 134(1), pages 95-128, September.
  7. 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).
  8. 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.
  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. 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.
  11. Tse, Y K & Tsui, Albert K C, 2002. "A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model with Time-Varying Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 351-62, July.
  12. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  13. 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.
  14. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 61-84, January.
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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. Audrino, Francesco, 2014. "Forecasting correlations during the late-2000s financial crisis: The short-run component, the long-run component, and structural breaks," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 43-60.
  3. Acatrinei, Marius & Gorun, Adrian & Marcu, Nicu, 2013. "A DCC-GARCH Model To Estimate the Risk to the Capital Market in Romania," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(1), pages 136-148, March.
  4. Matteo Barigozzi & Christian T. Brownlees & Giampiero M. Gallo & David Veredas, 2014. "Disentangling Systematic and Idiosyncratic Dynamics in Panels of Volatility Measures," Econometrics Working Papers Archive 2014_02, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti", revised Feb 2014.
  5. VAN BELLEGEM, Sébastien, 2011. "Locally stationary volatility modelling," CORE Discussion Papers 2011041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. 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.
  7. Golosnoy, Vasyl & Gribisch, Bastian & Liesenfeld, Roman, 2012. "The conditional autoregressive Wishart model for multivariate stock market volatility," Journal of Econometrics, Elsevier, vol. 167(1), pages 211-223.

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