Estimating Granger causality from fourier and wavelet transforms of time series data.

By M. Dhamala, Govindan Rangarajan, Mingzhou Ding. Physical Review Letters, 2007

323 citations recorded by the source corpus.

Experiments in many fields of science and engineering yield data in the form of time series. The Fourier and wavelet transform-based nonparametric methods are used widely to study the spectral characteristics of these time series data. Here, we extend the framework of nonparametric spectral methods to include the estimation of Granger causality spectra for assessing directional influences. We illustrate the utility of the proposed methods using synthetic data from network models consisting of interacting dynamical systems.

Subfields: Cognitive Neuroscience, Economics and Econometrics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/043cd83ae1901746b449743961fab137481f31b9

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Citations in the corpus

Hawkes Processes in Finance (2015, background): “In particular, the notion of Granger-causality has been extended to point-processes in [57, 25].”
Alpha-beta and gamma rhythms subserve feedback and feedforward influences among human visual cortical areas (2016, unknown): “Therefore, we used a non-parametric approach, which estimates GC directly from a factorization of the cross-spectral density (CSD) matrix (Dhamala et al., 2008).”
Complex network approaches to nonlinear time series analysis (2019, methodology): “Variousmethods have been proposed to extract the statistical associations fromdata, for instance, Pearson correlation,mutual information (including its timedelayed version) [24,25], Granger causality [26,27], transfer entropy [28,29], or methods for detecting coupling directions from time series dat”
Granger Causality: A Review and Recent Advances (2021, methodology): “Alternatively, one can also use tests in the spectral domain, using Fourier or wavelet representations (Geweke, 1982; Dhamala et al., 2008).”
Gamma-band synchronization in the neocortex: novel analysis methods and their application to sensory and motivational systems (2013, methodology): “Note that using matrix spectral factorization, the VAR model can also be obtained from the S in return (Dhamala et al., 2008).”
Analyzing information flow in brain networks with nonparametric Granger causality (2008, unknown): “From the minimum-phase spectral factor Ψ, noise covariance matrix Σ and minimum-phase transfer function H(f) can be obtained as X ¼ A 0 A T 0 ð5Þ and H ¼ WA À1 0 ð6Þ such that ΨΨ ⁎ = HΣH ⁎ (Dhamala et al., 2008).”
Detecting Causality in Complex Ecosystems (2012, unknown): “Applications typically use vector autoregression (VAR) (59, 60), conditional mutual information (CMI) (55, 61-70), or spectral methods (16, 57, 71-73).”
Analysis of sampling artifacts on the Granger causality analysis for topology extraction of neuronal dynamics (2014, methodology): “…out that these sampling issues arise from how discrete time series for the GC analysis are sampled from continuous time processes and they need to be addressed regardless of whether one uses a parametric method or a non-parametric method for the GC evaluation (Geweke, 1982; Dhamala et al., 2008).”