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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.

Suggested Citation

  • Hafner, Christian M. & Linton, Oliver, 2010. "Efficient estimation of a multivariate multiplicative volatility model," Journal of Econometrics, Elsevier, vol. 159(1), pages 55-73, November.
  • Handle: RePEc:eee:econom:v:159:y:2010:i:1:p:55-73
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    Cited by:

    1. Matteo Barigozzi & Brownlees Christian & Gallo Giampiero & David Veredas, "undated". "Disentangling systematic and idiosyncratic risks for large panels of assets," ULB Institutional Repository 2013/136237, ULB -- Universite Libre de Bruxelles.
    2. Bauwens, Luc & Braione, Manuela & Storti, Giuseppe, 2017. "A dynamic component model for forecasting high-dimensional realized covariance matrices," Econometrics and Statistics, Elsevier, vol. 1(C), pages 40-61.
    3. López Cabrera, Brenda & Schulz, Franziska, 2016. "Volatility linkages between energy and agricultural commodity prices," Energy Economics, Elsevier, vol. 54(C), pages 190-203.
    4. 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, August.
    5. BAUWENS, Luc & BRAIONE, Manuela & STORTI, Giuseppe, 2016. "Multiplicative Conditional Correlation Models for Realized Covariance Matrices," CORE Discussion Papers 2016041, 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. 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. Kotlyarova, Yulia & Schafgans, Marcia M. A. & Zinde‐Walsh, Victoria, 2011. "Adapting kernel estimation to uncertain smoothness," LSE Research Online Documents on Economics 42015, London School of Economics and Political Science, LSE Library.
    9. Proietti, Tommaso, 2014. "Exponential Smoothing, Long Memory and Volatility Prediction," MPRA Paper 57230, University Library of Munich, Germany.
    10. Barigozzi, Matteo & Brownlees, Christian & Gallo, Giampiero M. & Veredas, David, 2014. "Disentangling systematic and idiosyncratic dynamics in panels of volatility measures," Journal of Econometrics, Elsevier, vol. 182(2), pages 364-384.
    11. 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.
    12. Conrad, Christian & Stuermer, Karin, 2017. "On the economic determinants of optimal stock-bond portfolios: international evidence," Working Papers 0636, University of Heidelberg, Department of Economics.
    13. Matthieu Garcin & Clément Goulet, 2015. "Non-parameteric news impact curve: a variational approach," Documents de travail du Centre d'Economie de la Sorbonne 15086rr, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Feb 2017.
    14. VAN BELLEGEM, Sébastien, 2011. "Locally stationary volatility modelling," CORE Discussion Papers 2011041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    15. 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.
    16. Annastiina Silvennoinen & Timo Teräsvirta, 3108. "Consistency and asymptotic normality of maximum likelihood estimators of a multiplicative time-varying smooth transition correlation GARCH model," CREATES Research Papers 2017-28, Department of Economics and Business Economics, Aarhus University.
    17. Matthieu Garcin & Clément Goulet, 2015. "Non-parameteric news impact curve: a variational approach," Documents de travail du Centre d'Economie de la Sorbonne 15086r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Jul 2016.

    More about this item

    Keywords

    GARCH Kernel estimation Local stationarity Semiparametric;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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