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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

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

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  1. 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.
  2. BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen, 2003. "Multivariate GARCH models: a survey," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2003031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Pelletier, Denis, 2006. "Regime switching for dynamic correlations," Journal of Econometrics, Elsevier, Elsevier, vol. 131(1-2), pages 445-473.
  4. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  5. Roy van der Weide, 2002. "GO-GARCH: a multivariate generalized orthogonal GARCH model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 17(5), pages 549-564.
  6. 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, American Statistical Association, vol. 20(3), pages 351-62, July.
  7. Lanne, Markku & Saikkonen, Pentti, 2005. "A Multivariate Generalized Orthogonal Factor GARCH Model," MPRA Paper 23714, University Library of Munich, Germany.
  8. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 61-84, January.
  9. Pesaran, M. Hashem & Timmermann, Allan, 2004. "How costly is it to ignore breaks when forecasting the direction of a time series?," International Journal of Forecasting, Elsevier, Elsevier, vol. 20(3), pages 411-425.
  10. 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.
  11. Andrew J. Patton, 2006. "Estimation of multivariate models for time series of possibly different lengths," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 21(2), pages 147-173.
  12. Andrew J. Patton, 2006. "Modelling Asymmetric Exchange Rate Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, 05.
  13. 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.
  14. Juan Rodríguez-Poo & Oliver Linton, 2001. "Nonparametric factor analysis of residual time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, Springer, vol. 10(1), pages 161-182, June.
  15. Jondeau, Eric & Rockinger, Michael, 2006. "The Copula-GARCH model of conditional dependencies: An international stock market application," Journal of International Money and Finance, Elsevier, Elsevier, vol. 25(5), pages 827-853, August.
  16. Kawakatsu, Hiroyuki, 2006. "Matrix exponential GARCH," Journal of Econometrics, Elsevier, Elsevier, vol. 134(1), pages 95-128, September.
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Cited by:
  1. Barigozzi, Matteo & Brownlees, Christian & Gallo, Giampiero M. & Veredas, David, 2014. "Disentangling systematic and idiosyncratic dynamics in panels of volatility measures," Journal of Econometrics, Elsevier, Elsevier, vol. 182(2), pages 364-384.
  2. Tommaso Proietti, 2014. "Exponential Smoothing, Long Memory and Volatility Prediction," CEIS Research Paper 319, Tor Vergata University, CEIS, revised 30 Jul 2014.
  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, Institute for Economic Forecasting, vol. 0(1), pages 136-148, March.
  4. Michael Vogt, 2012. "Nonparametric regression for locally stationary time series," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP22/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. Luc Bauwens & Christian M. Hafner & Diane Pierret, 2013. "Multivariate Volatility Modeling Of Electricity Futures," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 743-761, 08.
  6. Golosnoy, Vasyl & Gribisch, Bastian & Liesenfeld, Roman, 2012. "The conditional autoregressive Wishart model for multivariate stock market volatility," Journal of Econometrics, Elsevier, Elsevier, vol. 167(1), pages 211-223.
  7. VAN BELLEGEM, Sébastien, 2011. "Locally stationary volatility modelling," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2011041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. 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, Elsevier, vol. 76(C), pages 43-60.

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