High-dimensional realized covariance estimation: a parametric approach

Abstract

We introduce a parametric dynamic factor specification for high-frequency financial data that simplifies considerably the estimation of the realized covariance matrix in high dimensions. The estimation method is tested in an empirical setting that emphasizes the effect of the curse of dimensionality. Compared to standard parametric approaches, our factor specification is computationally less demanding and provides statistically indistinguishable performances in standard risk management applications. The method is also assessed on Monte-Carlo simulations under several forms of misspecification.

Keywords:

• Realized covariance
• Risk management
• High-dimensions
• Epps effect

JEL Classification:

• C58
• D53
• D81

Acknowledgments

We thank the Editor and two anonymous Referees who helped us to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Supplemental data

Supplemental data for this article can be accessed online at http://dx.doi.org/10.1080/14697688.2022.2111267.

Notes

1 Hereafter, we will refer to this method as KEM, using the nomenclature of Corsi et al. (2015).

2 As a matter of fact, at a frequency of 5 min the fraction of missing observations collapses to zero for most assets.

3 In principle, the same analysis can be carried out with mean-variance portfolios. The latter depend on expected returns, which are notoriously difficult to estimate (Jagannathan and Ma 2003). To avoid spurious effects coming from the estimation of expected returns, we thus concentrate on GMV portfolios, which only rely on realized covariance estimates.

4 Note that the number of parameters in KEM is $d\left(\frac{d+3}{2}\right)$, whereas the number of parameters in KEM${}_r$ is $d(1+r)-r\left(\frac{r-1}{2}\right)$.

5 Alternatively to the flat forecast in equation (17(17) ${\widehat{RC}}_{t+1|t}={\hat{Z}}_t{\hat{\mathrm{\Lambda }}}_t{\hat{Z}}_t^{\mathrm{\top }}$(17) ), it is possible to compute the forecast by assuming a dynamic specification for $R{C}_t$, e.g. the HAR-DRD model of Oh and Patton (2018). We point out that the use of a different forecast method does not affect the relative performance of the realized covariance estimators examined here.

6 In the case of KEM${}_{r^{\ast }}$, we report the time needed to estimate the model after selecting $r^{\ast }$. If the BIC selection procedure is accounted for, the average computational time is on average approximately equal to the time required to estimate KEM.

7 The $5\times 5$ upper block of the factor loading matrix coincides with the identity matrix; see Section 2.2.