The effect of input parameters on detrended fluctuation analysis of theoretical and postural control data: data length significantly affects results

Date of Award


Degree Name

M.S. in Mechanical Engineering


Department of Mechanical and Aerospace Engineering


Advisor: Kimberly E. Bigelow


Biological variability is critical for healthy function and is present in all types of physiological movements. Variability exists on a spectrum in which the optimal amount falls between two extremes: a lack of variability indicating rigidity and limited adaptability and excessive variability indicating instability and random, uncontrolled motion. Traditionally, physiological variability has been quantified using linear measures, such as means, standard deviations, and ranges that ignore the temporal structure of the data. Nonlinear measures, however, take into account the temporal structure of the data and can be used to quantify the amount of order, predictability, regularity, and complexity associated with a system. It is believed that nonlinear analyses provide greater insight into human movement variability. Detrended fluctuation analysis (DFA) is a nonlinear analysis tool that has been used in posturography (i.e. postural control or balance) research. A limitation of DFA that has restricted its widespread use for analyzing physiological data, however, is its heavy dependence on input parameters used to determine the scaling exponent, a. Because the input parameters are selected by the researcher and little published guidance exists to aid in their selection, this research aimed to examine the effects of changing input parameters on DFA of theoretical time series with known values of a in order to determine best practices for their selection and improve the analysis's accuracy and robustness. To this end, theoretical time series were generated and subjected to DFA where the data length, the noise type cutoff range, and the size of the scaling region were varied. The value of a was determined for all combinations of input parameters and the effects of varying these parameters were explored using analysis of variance (ANOVA) techniques. The results of the ANOVAs indicated that data length significantly affected the results of DFA, while noise type cutoff ranges and scaling region did not. Based on the results of the ANOVAs as well as other published findings, the largest data length examined, a noise type cutoff range with the known values of a centered within the range, and large and medium sized scaling regions were selected as the optimum input parameters. This set of parameters was then applied to both theoretical time series and real posturography data sets in order to determine whether the refined input parameters produced statistically different results of DFA than did the traditional DFA method. ANOVAs were used to compare the a's calculated using traditional DFA methodology and the optimum input parameters, which suggested that the optimum input parameters yielded more theoretically accurate DFA results than did traditional DFA methodology. While this work was successful in providing some clarification on the requirements of input parameters for DFA, there is still room for future work to even more clearly define optimum DFA input parameters, particularly regarding data length and the size and location of the scaling region. Additional future work may also be done in order to better understand interactions that were present among the DFA method and scaling region factors and also the classification of the subject when the posturography data sets were examined.


Statistics, Biomechanics Data processing Methodology, Experimental design, Nonlinear theories, Quantitative research, Biomechanics, Mechanical Engineering, Nonlinear analysis, detrended fluctuation analysis, posturography, human movement variability, alpha scaling exponent

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Copyright © 2015, author