Joint Estimation of Conditional Mean and Covariance for Unbalanced Panels

2024-10-29

arXiv.org

AI Summary

This paper addresses the challenge of nonparametric joint estimation for large-scale, unbalanced, high-dimensional panel data exhibiting strong time-varying cross-sectional dependence. We propose the first provably consistent estimator with finite-sample guarantees for simultaneously modeling both the conditional mean function and the conditional covariance matrix. Our method departs from conventional two-step approaches and restrictive balanced-panel assumptions by integrating kernel regression, high-dimensional covariance shrinkage, and robust bandwidth selection—enabling flexible characterization of cross-sectional dependence driven by both macroeconomic and firm-level covariates. Empirical application to U.S. stock excess returns (1962–2021) reveals that idiosyncratic risk accounts for over 75% of cross-sectional variance on average, with statistically significant and economically robust results. The framework establishes a unified, reliable paradigm for joint heterogeneous modeling in unbalanced panels.

Technology Category

• Machine Learning: Kernel Methods
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI
• Security and Privacy: Large-scale security measurements

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.

Problem

• Estimates conditional mean and covariance for unbalanced panels
• Uses nonparametric kernel-based method for large datasets
• Analyzes time-varying dependencies in stock returns

Innovation

• Nonparametric kernel-based joint estimator
• Consistency and finite-sample guarantees
• Captures time-varying cross-sectional dependencies