title: Testing for Granger Causality in the Frequency Domain: A Phase Resampling Method.
abstract: This article introduces phase resampling, an existing but rarely used surrogate data method for making statistical inferences of Granger causality in frequency domain time series analysis. Granger causality testing is essential for establishing causal relations among variables in multivariate dynamic processes. However, testing for Granger causality in the frequency domain is challenging due to the nonlinear relation between frequency domain measures (e.g., partial directed coherence, generalized partial directed coherence) and time domain data. Through a simulation study, we demonstrate that phase resampling is a general and robust method for making statistical inferences even with short time series. With Gaussian data, phase resampling yields satisfactory type I and type II error rates in all but one condition we examine: when a small effect size is combined with an insufficient number of data points. Violations of normality lead to slightly higher error rates but are mostly within acceptable ranges. We illustrate the utility of phase resampling with two empirical examples involving multivariate electroencephalography (EEG) and skin conductance data.
authors.affiliation: a Human Development and Family Studies , Department of Human Ecology , University of California , Davis.
authors.forename: Siwei
authors.initials: S
authors.lastname: Liu
authors.affiliation: b Department of Human Development and Family Studies , The Pennsylvania State University.
authors.forename: Peter
authors.initials: P
authors.lastname: Molenaar
mesh_terms: D000465:Algorithms; D001921:Brain / Q000502:physiology; D002648:Child; D000068456:Clinical Studies as Topic; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D004569:Electroencephalography / Q000379:methods; D005712:Galvanic Skin Response; D006801:Humans; D008297:Male; D015999:Multivariate Analysis; D017711:Nonlinear Dynamics; D016011:Normal Distribution; D009788:Occupational Therapy; D010468:Perceptual Disorders / Q000503:physiopathology / Q000628:therapy; D012815:Signal Processing, Computer-Assisted
keywords: Frequency domain; Granger causality; generalized partial directed coherence; partial directed coherence; vector autoregressive model