A statistical mechanical analysis of postural sway using non-Gaussian FARIMA stochastic models

Postural sway is modeled using a fractional autoregressive integrated moving average (FARIMA) family of models: the center-of-pressure (COP) motion is viewed in terms of a self-similar, anti-persistent random-walk process, obtained by fractionally summating non-Gaussian random variables, whose correlation structure for small time lags is shaped by a linear time-invariant low-pass filter. The model parameters are: the strength of the stochastic driving, e.g., the root mean square (rms) value of the time-differenced COP motion; the DC gain, damping ratio and natural frequency of the filter; the Hurst exponent, which measures the random-walk anti-persistence magnitude. In the proposed modeling procedure, a graphical estimator for determining the Hurst exponent is cascaded to a method for matching autoregressive (AR) models to fractionally differenced COP motion via higher order cumulants. The effect of the presence or absence of vision on the model parameter values is discussed with regard to data from experiments on healthy young adults