Sailing in rough waters: Examining volatility of fMRI noise

Background: The assumption that functional magnetic resonance imaging (fMRI) noise has constant volatility has recently been challenged by studies examining heteroscedasticity arising from head motion and physiological noise. The present study builds on this work using latest methods from the field of financial mathematics to model fMRI noise volatility. Methods: Multi-echo phantom and human fMRI scans were used and realised volatility was estimated. The Hurst parameter H ∈ (0, 1), which governs the roughness/irregularity of realised volatility time series, was estimated. Calibration of H was performed pathwise, using well-established neural network calibration tools. Results: In all experiments the volatility calibrated to values within the rough case, H < 0.5, and on average fMRI noise was very rough with 0.03 < H < 0.05. Some edge effects were also observed, whereby H was larger near the edges of the phantoms. Discussion: The findings suggest that fMRI volatility is not only non-constant, but also substantially more irregular than a standard Brownian motion. Thus, further research is needed to examine the impact such pronounced oscillations in the volatility of fMRI noise have on data analyses.