Scaling invariance embedded in very short time series: A factorial moment based diffusion entropy approach

How to evaluate scaling behaviors in very short time series is still an open problem, in which the mechanism-dependence and the bias of estimation of a statistical quantity become critical. We propose a new method called factorial moment based diffusion entropy (FMDE). A theoretical derivation and extensive calculations show that it can give us a high-confident and unbiased evaluation of scaling exponent from a time series with a length of  ∼ 102. It provides a reliable method to monitor evolutionary behaviors of complex systems. As an illustration, it is used to monitor the fractal gait rhythm for a volunteer in six stride trials. We find rich patterns in its physiological state.