A model for interevent times with long tails and multifractality in human communications: An application to financial trading

TL;DR

This paper introduces a model based on Continuous Time Random Walks to explain the long-tailed and multifractal nature of interevent times in human communications, with a focus on financial trading data.

Contribution

It presents an analytical model that captures the multifractal structure of interevent times using superstatistics, advancing understanding of complex temporal patterns in human decision-making.

Findings

Empirical data shows multifractal behavior in financial inter-transaction times.

A stretched exponential kernel models the multifractality within a limited range.

A heuristic profile extends the model's applicability to broader regions.

Abstract

Social, technological and economic time series are divided by events which are usually assumed to be random albeit with some hierarchical structure. It is well known that the interevent statistics observed in these contexts differs from the Poissonian profile by being long-tailed distributed with resting and active periods interwoven. Understanding mechanisms generating consistent statistics have therefore become a central issue. The approach we present is taken from the Continuous Time Random Walk formalism and represents an analytical alternative to models of non-trivial priority that have been recently proposed. Our analysis also goes one step further by looking at the multifractal structure of the interevent times of human decisions. We here analyze the inter-transaction time intervals of several financial markets. We observe that empirical data describes a subtle multifractal behavior. Our model explains this structure by taking the pausing-time density in the form of a superstatistics where the integral kernel quantifies the heterogeneous nature of the executed tasks. An stretched exponential kernel provides a multifractal profile valid for a certain limited range. A suggested heuristic analytical profile is capable of covering a broader region.