Persistent and anti-persistent stride-to-stride fluctuations: an ARFIMA decomposition consistent with closed-loop sensorimotor control

Abstract

Stride-to-stride fluctuations in human walking carry a fractal correlation structure that reverses sign under external cueing: self-paced gait is persistent, whereas metronomic or visually cued gait is anti-persistent. Three decades of detrended fluctuation analysis (DFA) have established this reversal as a scaling-exponent shift, but DFA cannot distinguish genuine long-memory dynamics from short-memory autoregressive moving-average (ARMA) processes that produce the same apparent exponent. We fit the full eight-model ARFIMA(1,d,1) family to stride interval and stride speed series from three datasets (N = 70 subjects) spanning overground walking, fixed-speed treadmill walking, metronomic and visual cueing, and graded positional constraint. Model evidence is aggregated through BIC-based Schwarz weights, and the fractional differencing parameter d together with the autoregressive and moving-average coefficients phi and theta are estimated by Bayesian model averaging. Three findings emerge. (i) Long-memory specifications decisively outweigh ARMA alternatives under both persistent and anti-persistent conditions, establishing cued gait anti-persistence as a genuine fractional phenomenon. (ii) DFA alpha overestimates d + 0.5 by 0.25 to 0.34 units, a discrepancy jointly attributable to short-memory components that DFA conflates with long-memory persistence and to a finite-sample negative bias inherent to exact ML-ARFIMA estimation. (iii) The estimated (d, phi, theta) parameters are consistent with a corrective sensorimotor model in which a fractal intrinsic generator, a reactive feedback correction, and a motor-delay component together shape stride-to-stride fluctuations. Whether a single mechanistic model can account quantitatively for the observed parameter ranges across rhythmic, spatial, and unconstrained conditions is a question that the present analysis motivates but cannot alone resolve.