Coupled uncertainty provided by a multifractal random walker

TL;DR

This paper introduces a method to analyze the interaction of rare, critical events in paired time series using bivariate multifractal analysis, revealing how their coupling depends on individual system criticalities.

Contribution

It proposes a novel approach using bivariate multifractal random walk to study coupled criticality in non-Gaussian time series.

Findings

Coupled criticality varies with the criticality of individual series.

Application to financial and economic data demonstrates the method's effectiveness.

Rare events significantly influence the dependence structure between series.

Abstract

The aim here is to study the concept of pairing multifractality between time series possessing non-Gaussian distributions. The increasing number of rare events creates "criticality". We show how the pairing between two series is affected by rare events, which we call "coupled criticality". A method is proposed for studying the coupled criticality born out of the interaction between two series, using the bivariate multifractal random walk (BiMRW). This method allows studying dependence of the coupled criticality on the criticality of each individual system. This approach is applied to data sets of gold and oil markets, and inflation and unemployment.