Biophysics and Biosignals Laboratory, BioTech, University of Trento, 38060 Trento, Italy.
IEEE Trans Biomed Eng. 2010 Aug;57(8):1897-906. doi: 10.1109/TBME.2010.2042715. Epub 2010 Feb 18.
We introduce a new hypothesis-testing framework, based on surrogate data generation, to assess in the frequency domain, the concept of causality among multivariate (MV) time series. The approach extends the traditional Fourier transform (FT) method for generating surrogate data in a MV process and adapts it to the specific issue of causality. It generates causal FT (CFT) surrogates with FT modulus taken from the original series, and FT phase taken from a set of series with causal interactions set to zero over the direction of interest and preserved over all other directions. Two different zero-setting procedures, acting on the parameters of a MV autoregressive (MVAR) model fitted on the original series, were used to test the null hypotheses of absence of direct causal influence (CFTd surrogates) and of full (direct and indirect) causal influence (CFTf surrogates), respectively. CFTf and CFTd surrogates were utilized in combination with the directed coherence (DC) and the partial DC (PDC) spectral causality estimators, respectively. Simulations reproducing different causality patterns in linear MVAR processes demonstrated the better accuracy of CFTf and CFTd surrogates with respect to traditional FT surrogates. Application on real MV biological data measured from healthy humans, i.e., heart period, arterial pressure, and respiration variability, as well as multichannel EEG signals, showed that CFT surrogates disclose causal patterns in accordance with expected cardiorespiratory and neurophysiological mechanisms.
我们引入了一种新的基于替代数据生成的假设检验框架，用于在频域中评估多元（MV）时间序列之间的因果关系概念。该方法扩展了传统的傅里叶变换（FT）方法，用于在 MV 过程中生成替代数据，并将其适应于因果关系的特定问题。它生成因果 FT（CFT）替代数据，FT 模数以原始序列的 FT 模数以原始系列的 FT 相位，并且从具有因果相互作用的一系列系列中获取 FT 相位，并且将其在感兴趣的方向上设置为零，并在所有其他方向上保留。使用两种不同的零设置过程，作用于在原始系列上拟合的 MV 自回归（MVAR）模型的参数，分别用于测试不存在直接因果影响的零假设（CFTd 替代数据）和存在完全（直接和间接）因果影响的零假设（CFTf 替代数据）。CFTf 和 CFTd 替代数据分别与有向相干性（DC）和部分 DC（PDC）谱因果估计器结合使用。在线性 MVAR 过程中复制不同因果关系模式的模拟表明，CFTf 和 CFTd 替代数据相对于传统 FT 替代数据具有更高的准确性。对来自健康人类的真实 MV 生物数据（即心率、动脉压和呼吸变异性以及多通道 EEG 信号）的应用表明，CFT 替代数据揭示了与预期的心肺和神经生理机制一致的因果关系模式。
