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Modelling multivariate volatilities via conditionally uncorrelated components

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  • Jianqing Fan
  • Mingjin Wang
  • Qiwei Yao

Abstract

Summary. We propose to model multivariate volatility processes on the basis of the newly defined conditionally uncorrelated components (CUCs). This model represents a parsimonious representation for matrix‐valued processes. It is flexible in the sense that each CUC may be fitted separately with any appropriate univariate volatility model. Computationally it splits one high dimensional optimization problem into several lower dimensional subproblems. Consistency for the estimated CUCs has been established. A bootstrap method is proposed for testing the existence of CUCs. The methodology proposed is illustrated with both simulated and real data sets.

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  • 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.
  • Handle: RePEc:bla:jorssb:v:70:y:2008:i:4:p:679-702
    DOI: 10.1111/j.1467-9868.2008.00654.x
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    Cited by:

    1. Sébastien Laurent & Jeroen V. K. Rombouts & Francesco Violante, 2012. "On the forecasting accuracy of multivariate GARCH models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 934-955, September.
    2. Peter Boswijk, H. & van der Weide, Roy, 2011. "Method of moments estimation of GO-GARCH models," Journal of Econometrics, Elsevier, vol. 163(1), pages 118-126, July.
    3. Creal, Drew & Koopman, Siem Jan & Lucas, André, 2011. "A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(4), pages 552-563.
    4. Marc Hallin & Luis K. Hotta & João H. G Mazzeu & Carlos Cesar Trucios-Maza & Pedro L. Valls Pereira & Mauricio Zevallos, 2019. "Forecasting Conditional Covariance Matrices in High-Dimensional Time Series: a General Dynamic Factor Approach," Working Papers ECARES 2019-14, ULB -- Universite Libre de Bruxelles.
    5. Trucíos, Carlos & Hotta, Luiz K. & Valls Pereira, Pedro L., 2019. "On the robustness of the principal volatility components," Journal of Empirical Finance, Elsevier, vol. 52(C), pages 201-219.
    6. Broda, Simon A. & Haas, Markus & Krause, Jochen & Paolella, Marc S. & Steude, Sven C., 2013. "Stable mixture GARCH models," Journal of Econometrics, Elsevier, vol. 172(2), pages 292-306.
    7. Darolles, Serge & Francq, Christian & Laurent, Sébastien, 2018. "Asymptotics of Cholesky GARCH models and time-varying conditional betas," Journal of Econometrics, Elsevier, vol. 204(2), pages 223-247.
    8. Peña, Daniel & González-Prieto, Ester & García-Ferrer, Antonio, 2008. "A multivariate generalized independent factor GARCH model with an application to financial stock returns," DES - Working Papers. Statistics and Econometrics. WS ws087528, Universidad Carlos III de Madrid. Departamento de Estadística.
    9. Noureldin, Diaa & Shephard, Neil & Sheppard, Kevin, 2014. "Multivariate rotated ARCH models," Journal of Econometrics, Elsevier, vol. 179(1), pages 16-30.
    10. Claudio, Morana, 2015. "Semiparametric Estimation of Multivariate GARCH Models," Working Papers 317, University of Milano-Bicocca, Department of Economics, revised 10 Dec 2015.
    11. Marc Hallin & Carlos Trucíos, 2020. "Forecasting Value-at-Risk and Expected Shortfall in Large Portfolios: a General Dynamic Factor Approach," Working Papers ECARES 2020-50, ULB -- Universite Libre de Bruxelles.
    12. García-Ferrer, Antonio & González-Prieto, Ester & Peña, Daniel, 2012. "A conditionally heteroskedastic independent factor model with an application to financial stock returns," International Journal of Forecasting, Elsevier, vol. 28(1), pages 70-93.
    13. Zhang, Yongli & Rolling, Craig & Yang, Yuhong, 2021. "Estimating and forecasting dynamic correlation matrices: A nonlinear common factor approach," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    14. Morana, Claudio, 2019. "Regularized semiparametric estimation of high dimensional dynamic conditional covariance matrices," Econometrics and Statistics, Elsevier, vol. 12(C), pages 42-65.
    15. Li, Weiming & Gao, Jing & Li, Kunpeng & Yao, Qiwei, 2016. "Modelling multivariate volatilities via latent common factors," LSE Research Online Documents on Economics 68121, London School of Economics and Political Science, LSE Library.
    16. Gian Piero Aielli & Massimiliano Caporin, 2015. "Dynamic Principal Components: a New Class of Multivariate GARCH Models," "Marco Fanno" Working Papers 0193, Dipartimento di Scienze Economiche "Marco Fanno".
    17. repec:hrv:faseco:34650305 is not listed on IDEAS
    18. Chrétien, Stéphane & Ortega, Juan-Pablo, 2014. "Multivariate GARCH estimation via a Bregman-proximal trust-region method," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 210-236.

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