Higher-order analysis within Weierstrass hierarchical walks
We developed the Weierstrass walks (WW) model which describes both stationary and non-stationary stochastic time series. This model is a kind of Levy walks, where we assume a hierarchical, self-similar in a stochastic sense, spatio-temporal representation of main probabability densities. We consider a fractional random walk of a walker having, in general, different velocities between successive turning points. The WW model makes it possible to analyze the structure of the Hurst exponent. The analysis uses both the diffusion and the super Burnett coefficients. We constructed the diffusion phase diagram which distinguishes regions occupied by classes of different universality. We study only such classes which are characteristic of stationary situations. We thus have a model ready for describing of time series presented in the form of moving averages. (C) 2002 Elsevier Science B.V. All rights reserved.
weierstrass walks levy walks hurst exponent kurtosis