An asymptotic theory for cross-correlation between auto-correlated sequences and its application on neuroimaging data

Abstract

Background: Functional connectivity is among the most important tools to study brain. The correlation coefficient, between time series of different brain areas, is the most popular method to quantify functional connectivity. Correlation coefficient in practical use assumes the data to be temporally independent. However, the time series data of brain can manifest significant temporal auto-correlation.

New method: A widely applicable method is proposed for correcting temporal auto-correlation. We considered two types of time series models: (1) auto-regressive-moving-average model, (2) nonlinear dynamical system model with noisy fluctuations, and derived their respective asymptotic distributions of correlation coefficient. These two types of models are most commonly used in neuroscience studies. We show the respective asymptotic distributions share a unified expression.

Result: We have verified the validity of our method, and shown our method exhibited sufficient statistical power for detecting true correlation on numerical experiments. Employing our method on real dataset yields more robust functional network and higher classification accuracy than conventional methods.

Comparison with existing methods: Our method robustly controls the type I error while maintaining sufficient statistical power for detecting true correlation in numerical experiments, where existing methods measuring association (linear and nonlinear) fail.

Conclusions: In this work, we proposed a widely applicable approach for correcting the effect of temporal auto-correlation on functional connectivity. Empirical results favor the use of our method in functional network analysis.

Keywords: Asymptotic distribution; Correcting temporal auto-correlation effect; Correlation coefficient; Functional connectivity; Higher classification accuracy.