Mathematical Proof of the Synthetic Running Correlation Coefficient and Its Ability to Reflect Temporal Variations in Correlation
Mathematical Proof of the Synthetic Running Correlation Coefficient and Its Ability to Reflect Temporal Variations in Correlation
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DOI：
10.1007/s11802-021-4826-9
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发表时间：
2021-05
影响因子：
1.6
通讯作者：
Jinping Zhao;Yong Cao;Yanlong Shi;Xin Wang
中科院分区：
文献类型：
--
作者：
Jinping Zhao;Yong Cao;Yanlong Shi;Xin Wang
运行相关系数（RCC）用于捕获两个时间序列之间相关性的时间变化。局部运行相关系数（LRCC）是一种广泛使用的算法，它直接将皮尔逊相关应用于时间窗口。2018年提出了一种称为合成运行相关系数（SRCC）的新算法，并证明了其合理性和可用性，但该算法缺乏理论论证。本文从理论上证明了SRCC。RCC只有在不同时间的值可以比较时才有意义。首先，全球平均值被证明是用于比较的唯一标准量。SRCC是唯一符合可比性标准的RCC。利用统计方法推导了LRCC和SRCC之间的关系，并通过在LRCC算法中加入约束条件得到SRCC。将时间波动分为高频和低频信号揭示了LRCC仅反映高频信号的相关性;相反，SRCC同时反映高频和低频信号的相关性。因此，SRCC是计算RCC的合适方法。
The running correlation coefficient (RCC) is useful for capturing temporal variations in correlations between two time series. The local running correlation coefficient (LRCC) is a widely used algorithm that directly applies the Pearson correlation to a time window. A new algorithm called synthetic running correlation coefficient (SRCC) was proposed in 2018 and proven to be reasonable and usable; however, this algorithm lacks a theoretical demonstration. In this paper, SRCC is proven theoretically. RCC is only meaningful when its values at different times can be compared. First, the global means are proven to be the unique standard quantities for comparison. SRCC is the only RCC that satisfies the comparability criterion. The relationship between LRCC and SRCC is derived using statistical methods, and SRCC is obtained by adding a constraint condition to the LRCC algorithm. Dividing the temporal fluctuations into high- and low-frequency signals reveals that LRCC only reflects the correlation of high-frequency signals; by contrast, SRCC reflects the correlations of high- and low-frequency signals simultaneously. Therefore, SRCC is the appropriate method for calculating RCCs.