  A variety of resting state neuroimaging data tend to exhibit fractal behavior
where its power spectrum follows power-law scaling. Resting state functional
connectivity is significantly influenced by fractal behavior which may not
directly originate from neuronal population activities of the brain. To
describe the fractal behavior, we adopted the fractionally integrated process
(FIP) model instead of the fractional Gaussian noise (FGN) since the FIP model
covers more general aspects of fractality than the FGN model. We also introduce
a novel concept called the nonfractal connectivity which is defined as the
correlation of short memory independent of fractal behavior, and compared it
with the fractal connectivity which is an asymptotic wavelet correlation. We
propose several wavelet-based estimators of fractal connectivity and nonfractal
connectivity for a multivariate fractionally integrated noise (mFIN). The
performance of these estimators was evaluated through simulation studies and
the analyses of resting state functional MRI data of the rat brain.
