Identifying relationships among stochastic processes is a key goal in disciplines that deal with complex temporal systems, such as economics. While the standard toolkit for multivariate time series analysis has many advantages, it can be difficult to capture nonlinear dynamics using linear vector autoregressive models. This difficulty has motivated the development of methods for variable selection, causal discovery, and graphical modeling for nonlinear time series, which routinely employ nonparametric tests for conditional independence. In this paper, we introduce the first framework for conditional independence testing that works with a single realization of a nonstationary nonlinear process. The key technical ingredients are time-varying nonlinear regression, time-varying covariance estimation, and a distribution-uniform strong Gaussian approximation.

翻译：识别随机过程之间的关系是处理复杂时序系统学科（如经济学）的核心目标。虽然多变量时间序列分析的标准工具集具有诸多优势，但使用线性向量自回归模型难以捕捉非线性动态。这一困难推动了非线性时间序列变量选择、因果发现和图模型方法的发展，这些方法通常采用非参数条件独立性检验。本文提出了首个适用于非平稳非线性过程单次实现的条件独立性检验框架。其关键技术要素包括时变非线性回归、时变协方差估计以及分布均匀的强高斯逼近。