标题： 具有多变量非平稳非线性时间序列单个实现的条件独立性检验 显示英文标题

标题： Conditional independence testing with a single realization of a multivariate nonstationary nonlinear time series

摘要： 识别随机过程之间的关系是许多领域的一个核心目标，例如经济学。 虽然多变量时间序列分析的标准工具包有许多优点，但使用线性向量自回归模型很难捕捉非线性动态。 这种困难促使了用于非线性时间序列的因果发现和变量选择方法的发展，这些方法通常采用条件独立性检验。 在本文中，我们引入了第一个适用于非平稳非线性过程单个实现的条件独立性检验框架。 我们还展示了如何利用我们的框架进行独立性检验。 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的估计，以及分布统一的强高斯近似。 显示英文摘要

摘要： 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.