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Efficient estimation of a multivariate multiplicative volatility model

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  • Christian M. Hafner

    ()
    (Université catholique de Louvain - Université Catholique de Louvain)

  • Oliver Linton

    ()
    (Department of Economics - London School of Economics)

Abstract

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

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Bibliographic Info

Paper provided by HAL in its series Post-Print with number peer-00732539.

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Date of creation: 15 Sep 2010
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Publication status: Published, Journal of Econometrics, 2010, 159, 1, 55
Handle: RePEc:hal:journl:peer-00732539

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Related research

Keywords: C12; C13; C14; GARCH; Kernel estimation; Local stationarity; Semiparametric;

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References

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  1. Pelletier, Denis, 2006. "Regime switching for dynamic correlations," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 445-473.
  2. Kawakatsu, Hiroyuki, 2006. "Matrix exponential GARCH," Journal of Econometrics, Elsevier, vol. 134(1), pages 95-128, September.
  3. 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.
  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. Andrew Patton, 2004. "Modelling Asymmetric Exchange Rate Dependence," Working Papers wp04-04, Warwick Business School, Finance Group.
  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. 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.
  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. 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.
  10. 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.
  11. 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).
  12. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  13. 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.
  14. 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.
  15. 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, vol. 20(3), pages 411-425.
  16. 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, vol. 10(1), pages 161-182, June.
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Citations

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Cited by:
  1. 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.
  2. 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.
  3. 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.
  4. Proietti, Tommaso, 2014. "Exponential Smoothing, Long Memory and Volatility Prediction," MPRA Paper 57230, University Library of Munich, Germany.
  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. 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.
  7. 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.
  8. 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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