ARFIMA study reveals hidden long-memory patterns in human gait control

Philippe Terrier's new paper on arXiv (2604.24365) tackles a three-decade-old puzzle: why self-paced walking shows persistent (positive correlation) stride fluctuations, while metronome or visual-cued walking becomes anti-persistent (negative correlation). Earlier work using detrended fluctuation analysis (DFA) attributed this to a shift in the scaling exponent, but DFA cannot distinguish between genuine long-memory (fractional) dynamics and short-memory ARMA processes that mimic the same exponent. Terrier fits the full ARFIMA(1,d,1) family to stride interval and speed series from 70 subjects across overground, treadmill, cued, and constrained conditions. Using Bayesian model averaging and BIC-based Schwarz weights, he shows that long-memory models decisively outperform ARMA alternatives for both persistent and anti-persistent conditions.

Three key findings emerge. First, anti-persistence under external cueing is a genuine fractional phenomenon, not a statistical artifact. Second, DFA's alpha index consistently overestimates the true long-memory parameter d + 0.5 by 0.25–0.34 units due to conflated short-memory components and finite-sample negative bias in maximum-likelihood ARFIMA estimation. Third, the estimated (d, phi, theta) parameters align with a closed-loop sensorimotor control model where a fractal intrinsic generator (representing internal timing), a reactive feedback correction (responding to perturbations), and a motor delay component jointly produce the observed stride patterns. The study provides a reproducible analysis pipeline and opens the question of whether a single mechanistic model can quantitatively match the parameter ranges across all conditions.