用随机森林建模高维动态协方差，支持多条件变量。
High-Dimensional Dynamic Covariance Models with Random Forests
- 基于随机森林构建非参数动态协方差估计框架。
- 在高维下保持一致收敛，响应维度可随样本量亚指数增长。
- 适合金融时序等复杂高维动态建模场景。
本文提出一种新颖的非参数方法，用于在多个调节变量条件下估计高维动态协方差矩阵，该方法基于随机森林并具备坚实的理论保障。与传统静态方法不同，该动态非参数模型能有效捕捉分布异质性；与仅限单一调节变量的核平滑方法相比，本方法在全非参数框架下支持多变量调节。据我们所知，这是首个使用随机森林估计高维动态协方差矩阵的方法。在高维情形下，建立了统一一致性理论，提供非渐近误差率和模型选择性质，即使响应维度随样本量亚指数增长也成立。这些结果在一系列调节变量下均保持一致。通过模拟和股票数据集分析验证了方法的有效性，凸显其在高维复杂动态建模中的能力。
原文摘要 · Abstract (English)
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.
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