This article describes a refinement of recurrence analysis to determine the delay in the causal influence between a driver and a target, in the presence of additional perturbations affecting the time series of the response observable. The methodology is based on the definition of a new type of recurrence plots, the Conditional Joint Recurrence plot. The potential of the proposed approach resides in the great flexibility of recurrence plots themselves, which allows extending the technique to more than three quantities. Autoregressive time series, both linear and nonlinear, with different couplings and percentage of additive Gaussian noise have been investigated in detail, with and without outliers. The approach has also been applied to the case of synthetic periodic signals, representing realistic situations of synchronization experiments in thermonuclear fusion. The results obtained have been very positive; the proposed Conditional Joint Recurrence plots have always managed to identify the right interval of the causal influences and are very competitive with alternative techniques such as the Conditional Transfer Entropy.

中文翻译：

---

递归分析的改进以确定存在外部扰动时因果关系的时间延迟


本文描述了递归分析的改进，以确定在存在影响可观察响应时间序列的额外扰动的情况下，驾驶员和目标之间因果影响的延迟。该方法基于一种新型递归图的定义，即条件联合递归图。所提出方法的潜力在于递归图本身的巨大灵活性，这允许将该技术扩展到三个以上的数量。已经详细研究了具有不同耦合和加性高斯噪声百分比的线性和非线性自回归时间序列，无论是否存在异常值。该方法还应用于合成周期信号的情况，代表了热核聚变同步实验的现实情况。取得的成果非常积极；所提出的条件联合递归图始终能够成功地识别因果影响的正确区间，并且与条件转移熵等替代技术非常具有竞争力。