Functions for Estimating a (c)DCC-GARCH Model in large dimensions based on a publication by Engle et,al (2017) and Nakagawa et,al (2018). This estimation method is consist of composite likelihood method by Pakel et al. (2014) and (Non-)linear shrinkage estimation of covariance matrices by Ledoit and Wolf (2004,2015,2016).
To estimate the covariance matrix in financial time series, it is necessary consider two important aspects: the cross section and the time series. With regard to the cross section, we have the difficulty of correcting the biases of the sample covariance matrix eigenvalues in a large number of time series. With regard to the time series aspect, we have to account for volatility clustering and time-varying correlations. This package is implemented the improved estimation of the covariance matrix based on the following publications:
Aielli, Gian Piero. (2013). Dynamic conditional correlation: on properties and estimation. Journal of Business & Economic Statistics 31: 282-99. <doi:10.1080/07350015.2013.771027>
Engle, Robert F. (2002). Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business & Economic Statistics 20: 339-50. <doi:10.1198/073500102288618487>
Engle, Robert F, Olivier Ledoit, and Michael Wolf. (2017). Large dynamic covariance matrices. Journal of Business & Economic Statistics, 1-13. <doi:10.1080/07350015.2017.1345683>
Kei Nakagawa, Mitsuyoshi Imamura and Kenichi Yoshida. (2018). Risk-Based Portfolios with Large Dynamic Covariance Matrices. International Journal of Financial Studies, 6(2), 1-14. <doi:10.3390/ijfs6020052>
Ledoit, O. and Wolf, M. (2004). A well-conditioned estimator for large-dimensional covariance matrices. Journal of Multivariate Analysis, 88(2). <doi:10.1016/S0047-259X(03)00096-4>
Ledoit, O. and Wolf, M. (2012). Nonlinear shrinkage estimation of large-dimensional covariance matrices. Annals of Statistics, 40(2). <doi:10.1214/12-AOS989>
Ledoit, O. and Wolf, M. (2015). Spectrum estimation: a unified framework for covariance matrix estimation and PCA in large dimensions. Journal of Multivariate Analysis, 139(2). <doi:10.1016/j.jmva.2015.04.006>
Pakel, Cavit and Shephard, Neil and Sheppard, Kevin and Engle, Robert F. (2014). Fitting vast dimensional time-varying covariance models. Technical report <http://paneldataconference2015.ceu.hu/Program/Cavit-Pakel.pdf>
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