From Large to Vast: Composite Forecasting of Vast-Dimensional Realized Covariance Matrices Using Factor State-Space Models

46 Pages Posted: 6 Jan 2021 Last revised: 16 Feb 2021

See all articles by Jan P. Hartkopf

Jan P. Hartkopf

University of Cologne - Cologne Graduate School in Management, Economics and Social Sciences

Date Written: November 4, 2020

Abstract

We propose a dynamic factor state-space model for the prediction of high-dimensional realized covariance matrices of asset returns. Using a block LDL decomposition of the joint covariance matrix of assets and factors, we express the realized covariance matrix of the individual assets similar to an approximate factor model. We model the individual parts, i.e., the factor and residual covariances as well as the factor loadings, independently via a tractable state-space approach. This results in closed-form Matrix-F predictive densities for the distinct covariance elements and Student's t predictive densities for the factor loadings. In an out-of-sample forecasting and portfolio selection exercise we compare the performance of the proposed factor model under different specifications of the residual dynamics. These includes block diagonal residuals based on the GICS sector classifications and strict diagonality assumptions as well as combinations of both using linear shrinkage. We find that the proposed model performs very well in an empirical application to realized covariance matrices for 225 NYSE traded stocks using the well-known Fama-French factors and sector-specific factors represented by Exchange Traded Funds (ETFs).

Keywords: Factor model, realized covariance, state-space model, composite prediction

JEL Classification: C32, C38, C51, C58, G17

Suggested Citation

Hartkopf, Jan P., From Large to Vast: Composite Forecasting of Vast-Dimensional Realized Covariance Matrices Using Factor State-Space Models (November 4, 2020). Available at SSRN: https://ssrn.com/abstract=3721110 or http://dx.doi.org/10.2139/ssrn.3721110

Jan P. Hartkopf (Contact Author)

University of Cologne - Cologne Graduate School in Management, Economics and Social Sciences ( email )

Albertus-Magnus-Platz
Cologne, 50931
Germany

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