Hurst-Kolmogorov Process is a More Reliable and Statistically Powerful Alternative to Detrended Fluctuation Analysis for Estimating Hurst in Short Walking Trials

Abstract Background For decades, researchers have used Detrended Fluctuation Analysis (DFA) as a method to assess the temporal structure of gait variability through the Hurst exponent ( H) . However, DFA’s reliance on long time series limits reliability and reduces statistical power when applied to short walking trials, restricting its applicability. The Hurst-Kolmogorov process (HKp), an increasingly common algorithm, may offer more reliable and efficient estimates of the H in short walking trials. This study evaluated the reliability and statistical power of HKp versus DFA in estimating H from gait kinematics using short time series. Methods 119 healthy adults (34 young, 57 middle-aged, and 38 older) were sampled from the NONAN GaitPrint dataset. Each participant walked 9 four-minute trials per day over the course of two days, which were a week apart. H was estimated for stride interval, stride length, and the lower limb joint range of motion using DFA and HKp. Kinematic variables were calculated for time series ranging from 50 to 175 strides. Intraclass correlation coefficients (ICCs) were calculated between days using the average of 1 to 9 trials per day. Power estimations using simulated time series were performed to assess the ability of each method to detect group differences under varying effect sizes, sample sizes, trial numbers, and time series lengths. Results HKp achieved excellent reliability (ICC > 0.90) in short trials (<100 strides), whereas DFA rarely exceeded moderate reliability. Statistical power simulations demonstrated that HKp yielded higher power than DFA, particularly when fewer trials and subjects were available. A summary table is provided to guide sample size selection under different design conditions. Conclusion HKp offers a more reliable and statistically powerful alternative to DFA for estimating H in short walking trials. These findings support HKp as a practical tool for assessing the temporal structure of gait variability, improving feasibility in experimental and research settings.