A Rescaled Range Analysis of Random Events 1
Fotini Pallikari, Emil Boller · 1999
A b stract — The res c a l ed range st a t ist ical analysis was applied on sets of ran-dom numbers to demonstrate its potential in st u d y ing various types of biases and the presence of pe r i o d ical features. The data were generated by electro n-ic random number generators in psychokin es is tests. Accord ing to the th e o ry of Hurst, the res c a l ed range of in d e pendent random data is prop o rtional to th e s q u a re root of their number. In data which are not in d e pendent, the fractional Brownian motion model of Mandelbrot is useful in modeling their time series as pe rs istent or anti-pe rs istent. A weak pred o m inantly pe rs istent type of frac-tional Brownian motion in the data in d ic a t ed a bias which could not be dist in-g u is h ed from chance fluctuations after comp a r ison wi th computer simula t ed data. The basic steps for the application of this method, the variety of in fo r-mation it can provide and its limitations are dis c u s s ed. The method prov i d es a re la t i vely simple, yet ro b u st, technique for st u d y ing ano m a l i es in random e ve n t s. K e y w o rd s: a no m a l i es — fractional Brownian motion — Hurst exponent — pe r i o d ic i t i es — psychokin es is — res c a l ed range analysis 1.