Parametric Dependencies of Sliding Window Correlation

In this paper, we explore the dependence of sliding window correlation (SWC) results on different parameters of correlating signals. The SWC is extensively used to explore the dynamics of functional connectivity (FC) networks using resting-state functional MRI (rsfMRI) scans. These scanned signals often contain multiple amplitudes, frequencies, and phases. However, the exact values of these parameters are unknown. Two recent studies explored the relationship of window length and frequencies (minimum/maximum) in the correlating signals.

We extend the findings of these studies by using two deterministic signals with multiple amplitudes, frequencies, and phases. Afterward, we modulate one of the signals to introduce dynamics (nonstationarity) in their relationship. We also explore the relationship of window length and frequency band for real rsfMRI data.

For deterministic signals, the spurious fluctuations due to the method itself minimize, and the SWC estimates the stationary correlation when frequencies in the signals have specific relationship. For dynamic relationship also, the undesirable frequencies were removed under specific conditions for the frequencies. For real rsfMRI data, the SWC results varied with frequencies and window length.

In the absence of any "ground truth" for different parameters in real rsfMRI signals, the SWC with a constant window size may not be a reliable method to study the dynamics of the FC.

This study reveals the parametric dependencies of the SWC and its limitation as a method to analyze dynamics of FC networks in the absence of any ground truth.