Dynamic principal component CAW models for high-dimensional realized covariance matrices

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.

Keywords:

• Realized volatility
• Covariance matrix
• Spectral decomposition
• Time-series models

JEL Classification:

• C32
• C58
• G17

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. 2016, Engle et al. 2019, Sheppard and Xu 2019, for similar conventions).

2 The Matlab estimation files for the DPC-CAW model are available under https://github.com/mstollenwerk/dpc_caw.