Identifying relationships among stochastic processes is a core objective in many fields, 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 causal discovery and variable selection for nonlinear time series, which routinely employ 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. We also show how our framework can be used to test for independence. The key technical ingredients of our framework are time-varying nonlinear regression, estimation of local long-run covariance matrices of products of error processes, and a distribution-uniform strong Gaussian approximation.

翻译：识别随机过程之间的关系是经济学等多个领域的核心目标。虽然多变量时间序列分析的标准工具包具有诸多优势，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因果发现与变量选择方法的发展，这些方法常规性地采用条件独立性检验。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，并展示了该框架如何用于独立性检验。我们框架的关键技术要素包括时变非线性回归、误差过程乘积的局部长期协方差矩阵估计，以及分布一致强高斯逼近。