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Semiparametric Estimation of Multivariate GARCH Models

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  • Claudio, Morana

Abstract

The paper introduces a new simple semiparametric estimator of the conditional variance covariance and correlation matrix (SP-DCC). While sharing a similar sequential approach to existing dynamic conditional correlation (DCC) methods, SP-DCC has the advantage of not requiring the direct parameterization of the conditional covariance or correlation processes, therefore also avoiding any assumption on their long-run target. In the proposed framework, conditional variances are estimated by univariate GARCH models, for actual and suitably transformed series, in the first step; the latter are then nonlinearly combined in the second step, according to basic properties of the covariance and correlation operator, to yield nonparametric estimates of the various conditional covariances and correlations. Moreover, in contrast to available DCC methods, SP-DCC allows for straightforward estimation also for the non-symultaneous case, i.e., for the estimation of conditional cross-covariances and correlations, displaced at any time horizon of interest. A simple ex-post procedure, to ensure well behaved conditional covariance and correlation matrices, grounded on nonlinear shrinkage, is finally proposed. Due to its sequential implementation and scant computational burden, SP-DCC is very simple to apply and suitable for the modeling of vast sets of conditionally heteroskedastic time series.

Suggested Citation

  • Claudio, Morana, 2015. "Semiparametric Estimation of Multivariate GARCH Models," Working Papers 317, University of Milano-Bicocca, Department of Economics, revised 10 Dec 2015.
  • Handle: RePEc:mib:wpaper:317
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    References listed on IDEAS

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    1. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    2. Jianqing Fan & Mingjin Wang & Qiwei Yao, 2008. "Modelling multivariate volatilities via conditionally uncorrelated components," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 679-702.
    3. 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.
    4. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-131, February.
    5. I. D. Vrontos & P. Dellaportas & D. N. Politis, 2003. "A full-factor multivariate GARCH model," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 312-334, December.
    6. 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.
    7. Carol Alexander, 2002. "Principal Component Models for Generating Large GARCH Covariance Matrices," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 31(2), pages 337-359, July.
    8. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    9. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-359, October.
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    Cited by:

    1. Claudio Morana & Giacomo Sbrana, 2017. "Temperature anomalies, radiative forcing and ENSO," Working Paper series 17-06, Rimini Centre for Economic Analysis.
    2. Claudio, Morana, 2015. "The US$/€ exchange rate: Structural modeling and forecasting during the recent financial crises," Working Papers 321, University of Milano-Bicocca, Department of Economics, revised 28 Dec 2015.
    3. Karanasos, Menelaos & Xu, Yongdeng, 2017. "Matrix Inequality Constraints for Vector (Asymmetric Power) GARCH/HEAVY Models and MEM with spillovers: some New (Mixture) Formulations," Cardiff Economics Working Papers E2017/14, Cardiff University, Cardiff Business School, Economics Section.
    4. repec:eee:ecmode:v:64:y:2017:i:c:p:82-96 is not listed on IDEAS
    5. Morana, Claudio, 2017. "Macroeconomic and financial effects of oil price shocks: Evidence for the euro area," Economic Modelling, Elsevier, vol. 64(C), pages 82-96.

    More about this item

    Keywords

    Multivariate GARCH model; dynamic conditional correlation; semiparametric estimation;

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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