title: Evaluation of scaling invariance embedded in short time series.
abstract: Scaling invariance of time series has been making great contributions in diverse research fields. But how to evaluate scaling exponent from a real-world series is still an open problem. Finite length of time series may induce unacceptable fluctuation and bias to statistical quantities and consequent invalidation of currently used standard methods. In this paper a new concept called correlation-dependent balanced estimation of diffusion entropy is developed to evaluate scale-invariance in very short time series with length ~10(2). Calculations with specified Hurst exponent values of 0.2,0.3,...,0.9 show that by using the standard central moving average de-trending procedure this method can evaluate the scaling exponents for short time series with ignorable bias (≤0.03) and sharp confidential interval (standard deviation ≤0.05). Considering the stride series from ten volunteers along an approximate oval path of a specified length, we observe that though the averages and deviations of scaling exponents are close, their evolutionary behaviors display rich patterns. It has potential use in analyzing physiological signals, detecting early warning signals, and so on. As an emphasis, the our core contribution is that by means of the proposed method one can estimate precisely shannon entropy from limited records.
authors.affiliation: Business School, University of Shanghai for Science and Technology, Shanghai, China.
authors.forename: Xue
authors.initials: X
authors.lastname: Pan
authors.affiliation: Business School, University of Shanghai for Science and Technology, Shanghai, China.
authors.forename: Lei
authors.initials: L
authors.lastname: Hou
authors.affiliation: Business School, University of Shanghai for Science and Technology, Shanghai, China; Computer Science Department, Masinde Muliro University of Science and Technology, Kakamega, Kenya.
authors.forename: Mutua
authors.initials: M
authors.lastname: Stephen
authors.affiliation: Business School, University of Shanghai for Science and Technology, Shanghai, China.
authors.forename: Huijie
authors.initials: H
authors.lastname: Yang
authors.affiliation: College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, China.
authors.forename: Chenping
authors.initials: C
authors.lastname: Zhu
mesh_terms: D000293:Adolescent; D000328:Adult; D000465:Algorithms; D003627:Data Interpretation, Statistical; D019277:Entropy; D006801:Humans; D015233:Models, Statistical; D008991:Monitoring, Physiologic / Q000379:methods*; D013997:Time Factors; D055815:Young Adult