Multifractality of the multiplicative autoregressive point processes

TL;DR

This paper investigates the multifractal properties of multiplicative autoregressive point process models that generate 1/f^b noise, revealing their capacity to produce multifractal signals unlike traditional models.

Contribution

It demonstrates that multiplicative autoregressive point processes inherently generate multifractal signals, expanding understanding of their applicability in modeling complex stochastic systems.

Findings

Multiplicative point processes produce multifractal signals.

Traditional 1/f^b noise signals are not multifractal.

The models differ from uncorrelated component sums with wide relaxation times.

Abstract

Multiplicative processes and multifractals have earned increased popularity in applications ranging from hydrodynamic turbulence to computer network traffic, from image processing to economics. We analyse the multifractality of the recently proposed point process models generating the signals exhibiting 1/f^b noise. The models may be used for modeling and analysis of stochastic processes in different systems. We show that the multiplicative point process models generate multifractal signals, in contrast to the formally constructed signals with 1/f^b noise and signals consisting of sum of the uncorrelated components with a wide-range distribution of the relaxation times.