Joint Estimation of Conditional Mean and Covariance for Unbalanced Panels

TL;DR

This paper introduces a nonparametric kernel-based method for jointly estimating conditional mean and covariance matrices in large, unbalanced panels, with applications to US stock returns.

Contribution

It presents a novel joint estimator with proven consistency and finite-sample guarantees for large unbalanced panel data.

Findings

Idiosyncratic risk accounts for over 75% of cross-sectional variance.

The estimator captures time-varying dependencies effectively.

Robust statistical and economic performance demonstrated.

Abstract

We develop a nonparametric, kernel-based joint estimator for conditional mean and covariance matrices in large and unbalanced panels. The estimator is supported by rigorous consistency results and finite-sample guarantees, ensuring its reliability for empirical applications. We apply it to an extensive panel of monthly US stock excess returns from 1962 to 2021, using macroeconomic and firm-specific covariates as conditioning variables. The estimator effectively captures time-varying cross-sectional dependencies, demonstrating robust statistical and economic performance. We find that idiosyncratic risk explains, on average, more than 75% of the cross-sectional variance.