Most of the metrics used for detecting a causal relationship among multiple time series ignore the effects of practical measurement impairments, such as finite sample effects, undersampling and measurement noise. It has been shown that these effects significantly impair the performance of the underlying causality test. In this paper, we consider the problem of sequentially detecting the causal relationship between two time series while accounting for these measurement impairments. In this context, we first formulate the problem of Granger causality detection as a binary hypothesis test using the norm of the estimates of the vector auto-regressive~(VAR) coefficients of the two time series as the test statistic. Following this, we investigate sequential estimation of these coefficients and formulate a sequential test for detecting the causal relationship between two time series. Finally via detailed simulations, we validate our derived results, and evaluate the performance of the proposed causality detectors.

翻译：大多数用于检测多时间序列因果关系的方法忽略了实际测量缺陷的影响，例如有限样本效应、欠采样和测量噪声。已有研究表明，这些影响会显著损害底层因果性检验的性能。本文考虑在计及这些测量缺陷的情况下，序贯检测两个时间序列之间因果关系的问题。在此背景下，我们首先将格兰杰因果关系检测问题表述为一个二元假设检验，并以两个时间序列的向量自回归系数估计的范数作为检验统计量。随后，我们研究了这些系数的序贯估计方法，并构建了用于检测两个时间序列因果关系的序贯检验。最后，通过详细的仿真验证了推导结果，并评估了所提因果性检测器的性能。