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

Referee: The claim that long-memory specifications 'decisively outweigh' ARMA alternatives rests on BIC weights computed only within the restricted ARFIMA(1,d,1) family (p,q ∈ {0,1}). If stride series contain higher-order short-memory structure (plausible under multi-delay sensorimotor feedback), the fractional d can absorb residual autocorrelation, inflating evidence for long memory. No residual diagnostics, higher-order ARFIMA comparisons, or out-of-sample checks are described.

Authors: The ARFIMA(1,d,1) family was deliberately restricted to the minimal orders that allow explicit separation of the fractional parameter d from short-memory coefficients phi and theta, following standard practice in the gait literature for parsimonious modeling. BIC selection within this family already penalizes unnecessary complexity. We acknowledge the absence of higher-order comparisons and residual diagnostics as a limitation that could be addressed in future work. We will add a supplementary section reporting Ljung-Box residual tests on the selected models and a brief discussion of the order restriction. revision: partial

Referee: The statement that estimated (d, phi, theta) values are 'consistent with' a corrective sensorimotor model (fractal generator + reactive feedback + motor delay) is presented as an interpretive mapping without an explicit derivation from model equations, simulation-based recovery tests, or falsifiable predictions that would distinguish this account from alternative explanations.

Authors: We agree that the sensorimotor mapping is interpretive rather than derived from first principles or validated via simulation recovery. The consistency claim rests on the observed parameter ranges (positive d, negative phi under cueing, theta reflecting delay) aligning with qualitative predictions from a closed-loop model. We will revise the abstract and discussion to label this explicitly as a hypothesis-generating interpretation and to note the lack of formal derivation or falsification tests, while retaining the parameter ranges as the primary statistical result. revision: yes

Referee: Preprocessing steps, stationarity checks, and synthetic-data validation for the ARFIMA fitting and model-averaging procedure are not reported. These details are required to confirm that the reported d ranges and DFA bias estimates are not artifacts of non-stationarity or estimation bias.

Authors: The full Methods section describes linear detrending, removal of initial transients, and stationarity verification via ADF and KPSS tests prior to fitting; synthetic ARFIMA series were used internally to calibrate the Bayesian model averaging procedure. To make these steps fully transparent, we will expand the Methods with explicit pseudocode for the preprocessing pipeline and add a supplementary figure demonstrating parameter recovery on simulated data with known d, phi, and theta values. revision: yes