Fractal connectivity of long-memory networks.
Using the multivariate long memory (LM) model and Taylor expansions, we find the conditions for convergence of the wavelet correlations between two LM processes on an asymptotic value at low frequencies. These mathematical results, and a least squares estimator of LM parameters, are validated in simulations and applied to neurophysiological (human brain) and financial market time series. Both brain and market systems had multivariate LM properties including a "fractal connectivity" regime of scales over which wavelet correlations were invariantly close to their asymptotic value. This analysis provides efficient and unbiased estimation of long-term correlations in diverse dynamic networks.
Achard
Sophie
S
Brain Mapping Unit and Behavioural & Clinical Neurosciences Institute, University of Cambridge, Cambridge, UK. sa428@cam.ac.uk
Bassett
Danielle S
DS
Meyer-Lindenberg
Andreas
A
Bullmore
Ed
E
D000328:Adult; D001921:Brain / Q000502:physiology; D019295:Computational Biology / Q000379:methods; D003198:Computer Simulation; D005260:Female; D017709:Fractals; D006801:Humans; D016018:Least-Squares Analysis; D015225:Magnetoencephalography; D008568:Memory; D008959:Models, Neurological; D015233:Models, Statistical; D008962:Models, Theoretical; D015999:Multivariate Analysis; D016571:Neural Networks, Computer