Evolution of Complex Systems and 1/f Noise: from Physics to Financial Markets
We introduce the stochastic multiplicative model of time intervals between the events, defining a multiplicative point process and analyze the statistical properties of the signal. Such a model system exhibits power-law spectral density S(f)~1/fβ, scaled as power of frequency for various values of β between 0.5 and 2. We derive explicit expressions for the power spectrum and other statistics and analyze the model system numerically. The specific interest of our analysis is related with the theoretical modeling of the nonlinear complex systems exhibiting fractal behavior and self-organization.
V. Gontis et al., "Evolution of Complex Systems and 1/f Noise: from Physics to Financial Markets ", Solid State Phenomena, Vols. 97-98, pp. 65-70, 2004