Coupled uncertainty provided by a multifractal random walker

• The coupled criticality between two systems is modeled by the bivariate multifractal random walk.
• This coupled criticality is generally directed.
• This coupled criticality is inversely proportional to the criticality of either of the systems.
• The coupled criticality can emerge when at least one of the systems posses a Gaussian distribution.

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.