Establishing Causality With Whitened Cross-Correlation Analysis

In many biomedical applications, it is important to determine whether two recorded signals have a causal relationship and, if so, what the nature of that relationship is. Many advanced techniques have been proposed to characterize this relationship, but in practice simple techniques such as cross-correlation analysis are used. Unfortunately, the traditional cross-correlation analysis is influenced by the autocorrelation of the signals as much as it is by the relationship between the signals. Practically, this results in the cross correlation suggesting that the signals are correlated over a broad range of lags. Prewhitening the signals overcomes this limitation and reveals the essentially causal relationship between the signals. This is a simple method that can also easily generalize cross-correlation analysis to nonstationary signals, which are frequently encountered in biomedical applications. This technique has been used in other fields, but remains mostly undiscovered in biomedical research. In the case of a purely causal relationship, we show that whitened cross-correlation analysis is equivalent to directly estimating the all-pass component of the transfer function that relates the signals. We give examples of this type of analysis applied to several biomedical applications to demonstrate some of the new insights and information that can be produced by this type of analysis.