Testing for Granger Causality in the Frequency Domain: A Phase Resampling Method.

Area of Science:

• Neuroscience
• Statistics
• Signal Processing

Background:

• Granger causality is vital for understanding causal relationships in multivariate dynamic systems.
• Frequency domain Granger causality testing is complex due to nonlinearities between time and frequency domain measures.
• Existing methods for frequency domain Granger causality lack robustness, especially with limited data.

Purpose of the Study:

• Introduce and validate phase resampling as a reliable surrogate data method for frequency domain Granger causality inference.
• Assess the performance of phase resampling across various conditions, including data length and distribution.
• Demonstrate the practical application of phase resampling using real-world neurophysiological data.

Main Methods:

• Phase resampling, a surrogate data technique, was applied to frequency domain time series analysis.
• A simulation study was conducted to evaluate statistical inference accuracy (Type I and II errors).
• The method was tested with Gaussian and non-Gaussian data, varying effect sizes and data lengths.

Main Results:

• Phase resampling demonstrated general robustness and accuracy in statistical inferences, even for short time series.
• Satisfactory error rates were observed with Gaussian data, except for small effect sizes and insufficient data points.
• Minor increases in error rates occurred with violations of normality, remaining within acceptable limits.

Conclusions:

• Phase resampling is a versatile and effective method for statistical inference in frequency domain Granger causality analysis.
• The technique shows promise for analyzing complex time series data, including electroencephalography (EEG) and skin conductance.
• Phase resampling provides a valuable tool for researchers investigating causal dynamics in multivariate systems.