Miwakeichi Fumikazu, Galka Andreas
Department of Statistical Modeling, The Institute of Statistical Mathematics, Tokyo 190-8562, Japan.
Statistical Science Program, Graduate Institute for Advanced Studies, SOKENDAI, Tokyo 190-8562, Japan.
Entropy (Basel). 2023 Jul 17;25(7):1070. doi: 10.3390/e25071070.
In this study, we present a thorough comparison of the performance of four different bootstrap methods for assessing the significance of causal analysis in time series data. For this purpose, multivariate simulated data are generated by a linear feedback system. The methods investigated are uncorrelated Phase Randomization Bootstrap (uPRB), which generates surrogate data with no cross-correlation between variables by randomizing the phase in the frequency domain; Time Shift Bootstrap (TSB), which generates surrogate data by randomizing the phase in the time domain; Stationary Bootstrap (SB), which calculates standard errors and constructs confidence regions for weakly dependent stationary observations; and AR-Sieve Bootstrap (ARSB), a resampling method based on AutoRegressive (AR) models that approximates the underlying data-generating process. The uPRB method accurately identifies variable interactions but fails to detect self-feedback in some variables. The TSB method, despite performing worse than uPRB, is unable to detect feedback between certain variables. The SB method gives consistent causality results, although its ability to detect self-feedback decreases, as the mean block width increases. The ARSB method shows superior performance, accurately detecting both self-feedback and causality across all variables. Regarding the analysis of the Impulse Response Function (IRF), only the ARSB method succeeds in detecting both self-feedback and causality in all variables, aligning well with the connectivity diagram. Other methods, however, show considerable variations in detection performance, with some detecting false positives and others only detecting self-feedback.
在本研究中，我们对四种不同的自抽样方法在评估时间序列数据因果分析显著性方面的性能进行了全面比较。为此，通过线性反馈系统生成多元模拟数据。所研究的方法包括：不相关相位随机化自抽样法（uPRB），它通过在频域中随机化相位来生成变量之间无互相关的替代数据；时间移位自抽样法（TSB），它通过在时域中随机化相位来生成替代数据；平稳自抽样法（SB），它为弱相依平稳观测值计算标准误差并构建置信区域；以及自回归筛分自抽样法（ARSB），一种基于自回归（AR）模型的重抽样方法，用于近似潜在的数据生成过程。uPRB方法能准确识别变量间的相互作用，但在某些变量中无法检测到自反馈。TSB方法尽管表现不如uPRB，但也无法检测到某些变量之间的反馈。SB方法给出了一致的因果关系结果，不过随着平均块宽度的增加，其检测自反馈的能力会下降。ARSB方法表现出卓越的性能，能准确检测所有变量的自反馈和因果关系。关于脉冲响应函数（IRF）的分析，只有ARSB方法成功检测到所有变量的自反馈和因果关系，与连通性图高度吻合。然而，其他方法在检测性能上表现出相当大的差异，有些检测到误报，有些则只检测到自反馈。
