High-Dimensional Dynamic Covariance Models with Random Forests

TL;DR

This paper presents a pioneering nonparametric approach using random forests to estimate high-dimensional dynamic covariance matrices with multiple covariates, offering theoretical guarantees and practical effectiveness.

Contribution

It introduces the first random forest-based method for high-dimensional dynamic covariance estimation with multiple covariates, supported by uniform consistency theory.

Findings

Method accurately estimates covariance matrices in simulations.

Effective in modeling complex financial data.

Provides nonasymptotic error bounds and model selection insights.

Abstract

This paper introduces a novel nonparametric method for estimating high-dimensional dynamic covariance matrices with multiple conditioning covariates, leveraging random forests and supported by robust theoretical guarantees. Unlike traditional static methods, our dynamic nonparametric covariance models effectively capture distributional heterogeneity. Furthermore, unlike kernel-smoothing methods, which are restricted to a single conditioning covariate, our approach accommodates multiple covariates in a fully nonparametric framework. To the best of our knowledge, this is the first method to use random forests for estimating high-dimensional dynamic covariance matrices. In high-dimensional settings, we establish uniform consistency theory, providing nonasymptotic error rates and model selection properties, even when the response dimension grows sub-exponentially with the sample size. These results hold uniformly across a range of conditioning variables. The method's effectiveness is demonstrated through simulations and a stock dataset analysis, highlighting its ability to model complex dynamics in high-dimensional scenarios.