Abstract
We propose a new dynamic principal component CAW model (DPC-CAW) for time-series of high-dimensional realized covariance matrices of asset returns (up to 100 assets). The model performs a spectral decomposition of the scale matrix of a central Wishart distribution and assumes independent dynamics for the principal components' variances and the eigenvector processes. A three-step estimation procedure makes the model applicable to high-dimensional covariance matrices. We analyze the finite sample properties of the estimation approach and provide an empirical application to realized covariance matrices for 100 assets. The DPC-CAW model has particularly good forecasting properties and outperforms its competitors for realized covariance matrices.
Acknowledgements
The authors thank two anonymous referees for their helpful and constructive comments. This work was partially performed on the computational resource ‘BwForCluster MLS&WISO’ funded by the Ministry of Science, Research and Arts and the Universities of the State of Baden-Württemberg, Germany, within the framework program bwHPC.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1 In this paper we follow the convention of labeling covariance matrices of up to ten assets as ‘small dimensional’ and covariance matrices of up to 100 assets as ‘high-dimensional’. We are not concerned with ‘vast-dimensional’ or ‘large-dimensional’ covariance matrices with more than 100 assets (compare e.g. Lunde et al. Citation2016, Engle et al. Citation2019, Sheppard and Xu Citation2019, for similar conventions).
2 The Matlab estimation files for the DPC-CAW model are available under https://github.com/mstollenwerk/dpc_caw.