Encyclopedia of Computational Neuroscience

2015 Edition
| Editors: Dieter Jaeger, Ranu Jung

Directed Spectral Methods

  • Adam B. BarrettEmail author
  • Anil K. Seth
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-6675-8_414


Directed spectral measures quantify, in the frequency domain, directed statistical interactions between time-series variables. Most commonly, the various measures are computed based on a (linear) multivariate autoregressive (MVAR) model of the data. The various methods quantify in different ways the strength of interaction terms in the Fourier transform of the MVAR model. While these methods are sometimes referred to as capturing “causal” or “effective” connectivity, they are most properly described as reflecting “directed functional connectivity” (Friston et al. 2013).

Detailed Description

For a multivariate n-channel process X( t) = [ X 1( t), X 2( t), …, X n( t)] T (with zero mean), the MVAR model is given by
$$ \boldsymbol{X}(t)={\displaystyle \sum_{k=1}^p{A}_k\cdot \boldsymbol{X}\left(t-k\right)+\epsilon (t)}, $$
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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Sackler Centre for Consciousness Science and Department of InformaticsUniversity of SussexBrightonUK