Sailing in rough waters: examining volatility of fMRI noise

Background: Functional resonance magnetic imaging (fMRI) noise is usually assumed to have constant volatility. However this assumption has been recently challenged in a few studies examining heteroscedasticity arising from head motion and physiological noise. However, to our knowledge no studies have studied heteroscedasticity in scanner noise. Thus the aim of this study was to estimate the smoothness of fMRI scanner noise using latest methods from the field of financial mathematics. Methods: A multi-echo fMRI scan was performed on a phantom using two 3 tesla MRI units. The echo times were used as intra-time point data to estimate realised volatility. Smoothness of the realised volatility processes is examined by estimating the Hurst parameter, a parameter H \in (0,1) governing the roughness (H older continuity) of paths in the rough Bergomi model, introduced in Bayer et al. (2016). The rough Bergomi model a member of the family of rough stochastic volatility models. A family of models which was recently popularised in mathematical finance by observations indicating that volatility in financial markets is best described by stochastic models where volatility can be modulated by the Hurst parameter $H$, which usually calibrates to values H\in(0,0.5) (the rough case), hence inspiring the name of the model family. In this work, calibration of the Hurst parameter H is performed pathwise, using recently developed neural network calibration tools. Results: In all experiments the volatility calibrates to values well within the rough case H