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Regularized semiparametric estimation of high dimensional dynamic conditional covariance matrices

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  • Morana, Claudio

Abstract

A three-step estimation strategy for dynamic conditional correlation (DCC) models is proposed. In the first step, conditional variances for individual and aggregate series are estimated by means of QML equation by equation. In the second step, conditional covariances are estimated by means of the polarization identity and conditional correlations are estimated by their usual normalization. In the third step, the two-step conditional covariance and correlation matrices are regularized by means of a new non-linear shrinkage procedure and optimally smoothed. Due to its scant computational burden, the proposed regularized semiparametric DCC model (RSP-DCC) allows to estimate high dimensional conditional covariance and correlation matrices. An application to global minimum variance portfolio is also provided, confirming that RSP-DCC is a simple and viable alternative to existing DCC models.

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  • Morana, Claudio, 2019. "Regularized semiparametric estimation of high dimensional dynamic conditional covariance matrices," Econometrics and Statistics, Elsevier, vol. 12(C), pages 42-65.
  • Handle: RePEc:eee:ecosta:v:12:y:2019:i:c:p:42-65
    DOI: 10.1016/j.ecosta.2019.04.001
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    1. 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.
    2. 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.
    3. Morana, Claudio & Sbrana, Giacomo, 2019. "Climate change implications for the catastrophe bonds market: An empirical analysis," Economic Modelling, Elsevier, vol. 81(C), pages 274-294.
    4. 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.
    5. 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.
    6. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    7. Claudio, Morana & Giacomo, Sbrana, 2017. "Some Financial Implications of Global Warming: An Empirical Assessment," Working Papers 377, University of Milano-Bicocca, Department of Economics, revised 25 Dec 2017.
    8. Weide, R. van der, 2002. "Generalized Orthogonal GARCH. A Multivariate GARCH model," CeNDEF Working Papers 02-02, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    9. 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.
    10. Robert F. Engle, 2016. "Dynamic Conditional Beta," Journal of Financial Econometrics, Oxford University Press, vol. 14(4), pages 643-667.
    11. Olivier Ledoit & Michael Wolf, 2017. "Nonlinear Shrinkage of the Covariance Matrix for Portfolio Selection: Markowitz Meets Goldilocks," The Review of Financial Studies, Society for Financial Studies, vol. 30(12), pages 4349-4388.
    12. Olivier Ledoit & Pedro Santa-Clara & Michael Wolf, 2003. "Flexible Multivariate GARCH Modeling with an Application to International Stock Markets," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 735-747, August.
    13. Nijman, Theo & Sentana, Enrique, 1996. "Marginalization and contemporaneous aggregation in multivariate GARCH processes," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 71-87.
    14. Gian Piero Aielli, 2013. "Dynamic Conditional Correlation: On Properties and Estimation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 282-299, July.
    15. repec:taf:jnlbes:v:30:y:2012:i:2:p:212-228 is not listed on IDEAS
    16. Lorenzo Cappiello & Robert F. Engle & Kevin Sheppard, 2006. "Asymmetric Dynamics in the Correlations of Global Equity and Bond Returns," Journal of Financial Econometrics, Oxford University Press, vol. 4(4), pages 537-572.
    17. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    18. 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, September.
    19. Massimiliano Caporin & Michael McAleer, 2013. "Ten Things you should know about DCC," Tinbergen Institute Discussion Papers 13-048/III, Tinbergen Institute.
    20. Giacomo Sbrana, 2012. "Aggregation and marginalization of GARCH processes: some further results," METRON, Springer;Sapienza Università di Roma, vol. 70(2), pages 165-172, August.
    21. Joong-Ho Won & Johan Lim & Seung-Jean Kim & Bala Rajaratnam, 2013. "Condition-number-regularized covariance estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 427-450, June.
    22. Massimiliano Caporin & Michael McAleer, 2013. "Ten Things You Should Know about the Dynamic Conditional Correlation Representation," Econometrics, MDPI, vol. 1(1), pages 1-12, June.
    23. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(1), pages 29-52, March.
    24. Castle, Jennifer & Shephard, Neil (ed.), 2009. "The Methodology and Practice of Econometrics: A Festschrift in Honour of David F. Hendry," OUP Catalogue, Oxford University Press, number 9780199237197.
    25. Claudio, Morana, 2015. "Semiparametric Estimation of Multivariate GARCH Models," Working Papers 317, University of Milano-Bicocca, Department of Economics, revised 10 Dec 2015.
    26. Robert F. Engle & Olivier Ledoit & Michael Wolf, 2019. "Large Dynamic Covariance Matrices," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(2), pages 363-375, April.
    27. Paolella, Marc S. & Polak, Paweł, 2015. "COMFORT: A common market factor non-Gaussian returns model," Journal of Econometrics, Elsevier, vol. 187(2), pages 593-605.
    28. 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.
    29. 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.
    30. 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.
    31. Cavit Pakel & Neil Shephard & Kevin Sheppard & Robert F. Engle, 2021. "Fitting Vast Dimensional Time-Varying Covariance Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(3), pages 652-668, July.
    32. McAleer, Michael & Chan, Felix & Hoti, Suhejla & Lieberman, Offer, 2008. "Generalized Autoregressive Conditional Correlation," Econometric Theory, Cambridge University Press, vol. 24(6), pages 1554-1583, December.
    33. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
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    Cited by:

    1. Li, Degui, 2024. "Estimation of Large Dynamic Covariance Matrices: A Selective Review," Econometrics and Statistics, Elsevier, vol. 29(C), pages 16-30.
    2. Billio, Monica & Caporin, Massimiliano & Frattarolo, Lorenzo & Pelizzon, Loriana, 2023. "Networks in risk spillovers: A multivariate GARCH perspective," Econometrics and Statistics, Elsevier, vol. 28(C), pages 1-29.
    3. Morana, Claudio & Sbrana, Giacomo, 2019. "Climate change implications for the catastrophe bonds market: An empirical analysis," Economic Modelling, Elsevier, vol. 81(C), pages 274-294.

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    More about this item

    Keywords

    Conditional covariance; Dynamic conditional correlation model; Semiparametric dynamic conditional correlation model; Multivariate GARCH;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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