Impact of series length on statistical precision and sensitivity of autocorrelation assessment in human locomotion

Long-range autocorrelations (LRA) are a robust feature of rhythmic movements, which may provide important information about neural control and potentially constitute a powerful marker of dysfunction. A clear difficulty associated with the assessment of LRA is that it requires a large number of cycles to generate reliable results. Here we investigate how series length impacts the reliability of LRA assessment. A total of 94 time series extracted from walking or cycling tasks were re-assessed with series length varying from 64 to 512 data points. LRA were assessed using an approach combining the rescaled range analysis or the detrended fluctuation analysis (Hurst exponent, H), along with the shape of the power spectral density (α exponent). The statistical precision was defined as the ability to obtain estimates for H and α that are consistent with their theoretical relationship, irrespective of the series length. The sensitivity consisted of testing whether significant differences between experimental conditions found in the original studies when considering 512 data points persisted with shorter series. We also investigate the use of evenly-spaced diffusion plots as a methodological improvement of original version of methods for short series. Our results show that the reliable assessment of LRA requires 512 data points, or no shorter than 256 data points provided that more robust methods are considered such as the evenly-spaced algorithms. Such series can be reasonably obtained in clinical populations with moderate, or even more severe, gait impairments and open the perspective to extend the use of LRA assessment as a marker of gait stability applicable to a broad range of locomotor disorders.