Dangers and uses of cross-correlation in analyzing time series in perception, performance, movement, and neuroscience: The importance of constructing transfer function autoregressive models
Dangers and uses of cross-correlation in analyzing time series in perception, performance, movement, and neuroscience: The importance of constructing transfer function autoregressive models
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DOI：
10.3758/s13428-015-0611-2
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发表时间：
2016-06-01
影响因子：
5.4
通讯作者：
Dunsmuir, William T. M.
中科院分区：
文献类型：
--
作者：
Dean, Roger T.;Dunsmuir, William T. M.
许多关于感知、表现、心理生理学和神经科学的文章试图通过评估时间序列的互相关性来将时间序列对联系起来。大多数此类序列都是单独自相关的：它们不包含独立值。鉴于这种情况，通常会毫无根据地依赖互相关作为关系指标（例如，指示物与响应、引导与跟随）。由于自相关，这种互相关可能表明虚假关系。考虑到这些危险，我们在这里模拟了如何以及为何会出现此类虚假结论，以提供解决这些问题的方法。我们表明，当以多种不同方式聚合多对序列进行互相关分析时，问题仍然存在。最后，即使是真正的互相关函数也无法回答关键的激励问题，例如序列之间是否存在可能的因果关系。因此，我们说明如何获得描述此类关系的传递函数，并通过任何真正的互相关来了解。我们通过两个具体示例（感知和性能各一个）以及所需 R 软件代码的关键元素来说明混淆和有意义的传递函数。该方法涉及自相关函数、平稳性的建立、预白化、互相关函数的自由度确定、格兰杰因果关系的评估以及自回归模型的开发。自相关还限制了时间序列对之间可能关系的其他度量的可解释性，例如互信息。我们强调，随着充分进行适当的分析，可能需要进一步的复杂性，并且可能还需要因果干预实验。
Many articles on perception, performance, psychophysiology, and neuroscience seek to relate pairs of time series through assessments of their cross-correlations. Most such series are individually autocorrelated: they do not comprise independent values. Given this situation, an unfounded reliance is often placed on cross-correlation as an indicator of relationships (e.g., referent vs. response, leading vs. following). Such cross-correlations can indicate spurious relationships, because of autocorrelation. Given these dangers, we here simulated how and why such spurious conclusions can arise, to provide an approach to resolving them. We show that when multiple pairs of series are aggregated in several different ways for a cross-correlation analysis, problems remain. Finally, even a genuine cross-correlation function does not answer key motivating questions, such as whether there are likely causal relationships between the series. Thus, we illustrate how to obtain a transfer function describing such relationships, informed by any genuine cross-correlations. We illustrate the confounds and the meaningful transfer functions by two concrete examples, one each in perception and performance, together with key elements of the R software code needed. The approach involves autocorrelation functions, the establishment of stationarity, prewhitening, the determination dof cross-correlation functions, the assessment of Granger causality, and autoregressive model development. Autocorrelation also limits the interpretability of other measures of possible relationships between pairs of time series, such as mutual information. We emphasize that further complexity may be required as the appropriate analysis is pursued fully, and that causal intervention experiments will likely also be needed.