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Efficient estimation of a multivariate multiplicative volatility model

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  • Hafner, Christian M.
  • Linton, Oliver

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

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 159 (2010)
Issue (Month): 1 (November)
Pages: 55-73

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Handle: RePEc:eee:econom:v:159:y:2010:i:1:p:55-73

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Web page: http://www.elsevier.com/locate/jeconom

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Keywords: GARCH Kernel estimation Local stationarity Semiparametric;

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  2. Andrew Patton, 2004. "Modelling Asymmetric Exchange Rate Dependence," Working Papers, Warwick Business School, Finance Group wp04-04, Warwick Business School, Finance Group.
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  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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).
  10. Lanne, Markku & Saikkonen, Pentti, 2007. "A Multivariate Generalized Orthogonal Factor GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 25, pages 61-75, January.
  11. 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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  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, Elsevier, vol. 25(5), pages 827-853, August.
  14. 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.
  15. Kawakatsu, Hiroyuki, 2006. "Matrix exponential GARCH," Journal of Econometrics, Elsevier, Elsevier, vol. 134(1), pages 95-128, September.
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Citations

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Cited by:
  1. Golosnoy, Vasyl & Gribisch, Bastian & Liesenfeld, Roman, 2010. "The conditional autoregressive wishart model for multivariate stock market volatility," Economics Working Papers 2010,07, Christian-Albrechts-University of Kiel, Department of Economics.
  2. 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.
  3. Tommaso Proietti, 2014. "Exponential Smoothing, Long Memory and Volatility Prediction," CEIS Research Paper 319, Tor Vergata University, CEIS, revised 30 Jul 2014.
  4. 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.
  5. 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).
  6. 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.
  7. 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.
  8. 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.

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