Multifractality in the Random Parameters Model

TL;DR

This paper investigates the multifractal properties of the Random Parameters model, revealing its scaling behavior and compatibility with stylized facts, thus enhancing understanding of covariance matrix structures in complex systems.

Contribution

It introduces an analysis of the multifractal structure and scaling properties of the Random Parameters model, extending its characterization beyond eigenvalue distribution.

Findings

Multifractal scaling structure observed in the model time series.

Model's properties align with known stylized facts.

Scaling of the probability density function analyzed at larger scales.

Abstract

The Random Parameters model was proposed to explain the structure of the covariance matrix in problems where most, but not all, of the eigenvalues of the covariance matrix can be explained by Random Matrix Theory. In this article, we explore other properties of the model, like the scaling of its PDF as one take larger scales. Special attention is given to the multifractal structure of the model time series, which revealed a scaling structure compatible with the known stylized facts for a reasonable choice of the parameter values.