Kernel-based methods are used in the context of Granger Causality to enable the identification of nonlinear causal relationships between time series variables. In this paper, we show that two state of the art kernel-based Granger Causality (GC) approaches can be theoretically unified under the framework of Kernel Principal Component Regression (KPCR), and introduce a method based on this unification, demonstrating that this approach can improve causal identification. Additionally, we introduce a Gaussian Process score-based model with Smooth Information Criterion penalisation on the marginal likelihood, and demonstrate improved performance over existing state of the art time-series nonlinear causal discovery methods. Furthermore, we propose a contemporaneous causal identification algorithm, fully based on GC, using the proposed score-based $GP_{SIC}$ method, and compare its performance to a state of the art contemporaneous time series causal discovery algorithm.

翻译：在格兰杰因果关系研究中，核方法被用于识别时间序列变量间的非线性因果关系。本文证明，两种先进的基于核的格兰杰因果分析方法可在核主成分回归的理论框架下实现统一，并基于此统一框架提出了一种新方法，证明该方法能提升因果识别能力。此外，我们提出了一种基于高斯过程的评分模型，该模型在边缘似然函数中引入平滑信息准则惩罚项，实验表明其性能优于现有先进的非线性时间序列因果发现方法。进一步地，我们提出了一种完全基于格兰杰因果关系的同期因果识别算法，该算法采用所提出的基于评分的$GP_{SIC}$方法，并将其性能与先进的同期时间序列因果发现算法进行了对比。