Averaging estimation for conditional covariance models

Abstract

Estimating conditional covariance matrices is important in statistics and finance. In this paper, we propose an averaging estimator for the conditional covariance, which combines the estimates of marginal conditional covariance matrices by Model Averaging MArginal Regression of Li, Linton, and Lu. This estimator avoids the “curse of dimensionality” problem that the local constant estimator of Yin et al. suffered from. We establish the asymptotic properties of the averaging weights and that of the proposed conditional covariance estimator. The finite sample performances are augmented by simulation. An application to portfolio allocation illustrates the practical superiority of the averaging estimator.

Keywords:

• Averaging estimation
• conditional covariance estimation
• curse of dimensionality
• marginal regression
• portfolio allocation

Acknowledgement

The author thanks the reviewer of this note for his/her highly constructive comments and suggestions that led me to improve the manuscript.