Chaos analysis of the time series data derived from human activities

Abstract

Various chaos analyses have been applied for the time series of several human activities. As a result of recurrence plot and power spectrum analyses, three rough classes of the transactions between companies, those between companies and individuals, and those between individuals can be refined according to the geometrical structure of an attractor into three more accurate categories: non-stationary, periodic and stochastic changes. In a stochastic one, the slope of the approximate straight line of the log-log graph of power spectrum density: β ≥ 1.26, and the recurrence plot of its attractor shows non-contiguous diagonal lines; in a periodic one, 0.770 ≤ β ≤ 1.25, equally-spaced diagonals; and in a non-stationary one, 0.108 ≤ β ≤ 0.389, ambiguous boundaries of domain.