D. Gilden, T. , and M. Mallon, 1/f noise in human cognition, Science, vol.267, issue.5205, pp.1837-1839, 1995.

J. M. Hausdorff, C. K. Peng, Z. Ladin, J. Y. Wei, and A. L. Goldberger, Is walking a random walk? Evidence for long-range correlations in stride interval of human gait, Journal of Applied Physiology, vol.78, issue.1, pp.349-358, 1995.

L. Lemoine, K. Torre, and D. Delignières, Testing for the presence of 1/f noise in continuation tapping data, Canadian Journal of Experimental Psychology/Revue Canadienne de Psychologie Expérimentale, vol.60, issue.4, pp.247-257, 2006.

C. Peng, J. Mietus, J. M. Hausdorff, S. Havlin, H. E. Stanley et al., Long-range anticorrelations and non-Gaussian behavior of the heartbeat, Physical Review Letters, vol.70, issue.9, pp.1343-1346, 1993.

J. M. Hausdorff, Gait dynamics in Parkinson's disease: common and distinct behavior among stride length, gait variability, and fractal-like scaling, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.19, issue.2, p.26113, 2009.

N. Hunt, D. Mcgrath, and N. Stergiou, e influence of auditory-motor coupling on fractal dynamics in human gait, Scientific Reports, vol.4, issue.1, p.5879, 2014.

J. P. Kaipust, D. Mcgrath, M. Mukherjee, and N. Stergiou, Gait variability is altered in older adults when listening to auditory stimuli with differing temporal structures, Annals of Biomedical Engineering, vol.41, issue.8, pp.1595-1603, 2013.

C. K. Rhea, A. W. Kiefer, S. E. D'andrea, W. H. Warren, and R. K. Aaron, Entrainment to a real time fractal visual stimulus modulates fractal gait dynamics, Human Movement Science, vol.36, pp.20-34, 2014.

D. Delignieres, S. Ramdani, L. Lemoine, K. Torre, M. Fortes et al., Fractal analyses for 'short' time series: a reassessment of classical methods, Journal of Mathematical Psychology, vol.50, issue.6, pp.525-544, 2006.

A. Eke, P. Herman, and J. B. Bassingthwaighte, Physiological time series: distinguishing fractal noises from motions, Pflügers Archiv: European Journal of Physiology, vol.439, issue.4, pp.403-415, 2000.

A. Eke, P. Herman, L. Kocsis, and L. R. Kozak, Fractal characterization of complexity in temporal physiological signals, Physiological Measurement, vol.23, issue.1, pp.1-38, 2002.

R. Jennane, R. Harba, and G. Jacquet, Analysis methods for fractional Brownian motion: theory and comparative results, Trait Signal, vol.18, pp.419-436, 2001.

R. B. Davies and D. S. Harte, Tests for Hurst effect, Biometrika, vol.74, issue.1, pp.95-101, 1987.

S. Fatichi, ARFIMA simulations, 2009.

D. Saupe, Algorithms for random fractals, e Science of Fractal Images, pp.71-136, 1988.

B. B. Mandelbrot and J. W. Van-ness, Fractional Brownian motions, fractional noises and applications, SIAM Review, vol.10, issue.4, pp.422-437, 1968.

R. F. Voss, 1/f (flicker) noise: a brief review, Proceedings of the 33rd Annual Symposium on Frequency Control, pp.40-46, 1979.

C. W. Granger and R. Joyeux, An introduction to longmemory time series models and fractional differencing, Journal of Time Series Analysis, vol.1, issue.1, pp.15-29, 1980.

M. S. Taqqu, V. Teverovsky, and W. Willinger, Estimators for long-range dependence: an empirical study, Fractals, vol.3, issue.4, pp.785-798, 1995.

P. Flandrin, On the spectrum of fractional Brownian motions, IEEE Transactions on Information eory, vol.35, issue.1, pp.197-199, 1989.

D. Delignières and V. Marmelat, eoretical and methodological issues in serial correlation analysis, Advances in Experimental Medicine and Biology, vol.782, pp.127-148, 2013.

G. E. Box, G. Jenkins, G. C. Reinsel, and G. M. Ljung, Time Series Analysis: Forecasting and Control, 1976.

M. Fortes, G. Ninot, and D. Delignières, e auto-regressive integrated moving average procedures: implications for adapted physical activity research, Adapted Physical Activity Quarterly, vol.22, issue.3, pp.221-236, 2005.

J. Beran, Statistics for Long-Memory Processes, 1994.

J. Beran, Y. Feng, S. Ghosh, and R. Kulik, Long-Memory Processes, 2013.

K. Torre, D. Delignières, and L. Lemoine, Detection of longrange dependence and estimation of fractal exponents through ARFIMA modelling, British Journal of Mathematical and Statistical Psychology, vol.60, issue.1, pp.85-106, 2007.

T. Stadnitski, Some critical aspects of fractality research, Nonlinear Dynamics, vol.16, pp.137-158, 2012.

D. Delignières, Correlation properties of (discrete) fractional Gaussian noise and fractional Brownian motion, Mathematical Problems in Engineering, vol.2015, 2015.

Z. M. Almurad and D. Delignières, Evenly spacing in detrended fluctuation analysis, Physica A: Statistical Mechanics and Its Applications, vol.451, pp.63-69, 2016.

P. F. Fougere, On the accuracy of spectrum analysis of red noise processes using maximum entropy and periodogram methods: simulation studies and application to geophysical data, Journal of Geophysical Research, vol.90, issue.A5, pp.4355-4366, 1985.

G. Inzelt, Maximum Likelihood Estimators of Stationary Univariate ARFIMA (p, d, q) Processes, 2011.

C. Diebolt and V. Guiraud, A note on long memory time series, Quality and Quantity, vol.39, issue.6, pp.827-836, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00278694

D. C. Caccia, D. Percival, M. J. Cannon, G. Raymond, and J. B. Bassingthwaighte, Analyzing exact fractal time series: evaluating dispersional analysis and rescaled range methods, Physica A: Statistical Mechanics and Its Applications, vol.246, issue.3-4, pp.609-632, 1997.

M. J. Cannon, D. B. Percival, D. C. Caccia, G. M. Raymond, and J. B. Bassingthwaighte, Evaluating scaled windowed variance methods for estimating the Hurst coefficient of time series, Physica A: Statistical Mechanics and Its Applications, vol.241, issue.3-4, pp.606-626, 1997.

D. Delignières, K. Torre, and P. Bernard, Transition from persistent to anti-persistent correlations in postural sway indicates velocity-based control, PLoS Computational Biology, vol.7, issue.2, p.1001089, 2011.

D. G. Stephen and J. Anastas, Fractal fluctuations in gaze speed visual search, Attention, Perception, and Psychophysics, vol.73, issue.3, pp.666-677, 2011.

D. Delignières, L. Lemoine, and K. Torre, Time intervals production in tapping and oscillatory motion, Human Movement Science, vol.23, issue.2, pp.87-103, 2004.

E. Wagenmakers, S. Farrell, and R. Ratcliff, Estimation and interpretation of 1/f? noise in human cognition, Psychonomic Bulletin and Review, vol.11, issue.4, pp.579-615, 2004.

G. Rangarajan and M. Ding, Integrated approach to the assessment of long range correlation in time series data, Physical Review E, vol.61, issue.5, pp.4991-5001, 2000.

J. A. Doornik and M. Ooms, A Package for Estimating, Forecasting, and Simulating Arfima Models: Arfima Package 1.0 for Ox, 1999.

M. Ooms and J. A. Doornik, Estimation, Simulation and Forecasting for Fractional Autoregressive Integrated Moving Average Models, Proceedings of the Fourth International Symposium in Computational Economics and Finance, 1998.

J. A. Doornik, Ox: An Object-Oriented Matrix Language, 2001.

K. Liu, Y. Chen, and X. Zhang, An evaluation of ARFIMA (autoregressive fractional integral moving average) programs, Axioms, vol.6, issue.4, p.16, 2017.

E. Wagenmakers, S. Farrell, and R. Ratcliff, Human cognition and a pile of sand: a discussion on serial correlations and self-organized criticality, Journal of Experimental Psychology: General, vol.134, issue.1, pp.108-116, 2005.

Z. M. Almurad, C. Roume, H. Blain, and D. Delignieres, Complexity matching: restoring the complexity of locomotion in older people through arm-in-arm walking, Frontiers in Physiology, vol.9, p.1766, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01976776

Z. M. Almurad, C. Roume, and D. Delignières, Complexity matching in side-by-side walking, Human Movement Science, vol.54, pp.125-136, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01839911

J. M. Hausdorff, S. L. Mitchell, and R. Firtion, Altered fractal dynamics of gait: reduced stride-interval correlations with aging and Huntington's disease, Journal of Applied Physiology, vol.82, issue.1, pp.262-269, 1997.

N. A. Kuznetsov and C. K. Rhea, Power considerations for the application of detrended fluctuation analysis in gait variability studies, PLoS One, vol.12, issue.3, 2017.

D. Delignieres and V. Marmelat, Fractal fluctuations and complexity: current debates and future challenges, Critical Reviews in Biomedical Engineering, vol.40, issue.6, pp.485-500, 2012.