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Assessing Granger Non-Causality Using Nonparametric Measure of Conditional Independence

机译：使用条件独立性的非参数测度评估格兰杰非因果关系

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In recent years, Granger causality has become a popular method in a variety of research areas including engineering, neuroscience, and economics. However, despite its simplicity and wide applicability, the linear Granger causality is an insufficient tool for analyzing exotic stochastic processes such as processes involving non-linear dynamics or processes involving causality in higher order statistics. In order to analyze such processes more reliably, a different approach toward Granger causality has become increasingly popular. This new approach employs conditional independence as a tool to discover Granger non-causality without any assumption on the underlying stochastic process. This paper discusses the concept of discovering Granger non-causality using measures of conditional independence, and proposes a novel measure of conditional independence. In brief, the proposed approach estimates the conditional distribution function through a kernel based least square regression approach. This paper also explores the strengths and weaknesses of the proposed method compared to other available methods, and provides a detailed comparison of these methods using a variety of synthetic data sets.
机译：近年来，格兰杰因果关系已成为工程，神经科学和经济学等各种研究领域的流行方法。但是，尽管它具有简单性和广泛的适用性，但线性Granger因果关系还是不足以用来分析外来随机过程，例如涉及非线性动力学的过程或涉及高阶统计中因果关系的过程。为了更可靠地分析此类过程，针对格兰杰因果关系的另一种方法已变得越来越流行。这种新方法将条件独立性用作发现格兰杰非因果关系的工具，而无需对基础随机过程进行任何假设。本文讨论了使用条件独立性度量发现格兰杰非因果关系的概念，并提出了一种新的条件独立性度量。简而言之，所提出的方法通过基于核的最小二乘回归方法来估计条件分布函数。本文还探讨了与其他可用方法相比，该方法的优缺点，并使用各种综合数据集对这些方法进行了详细的比较。

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