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

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.

25 pages, 10 colored figures

References in corpus (12)

• Modeling bursts and heavy tails in human dynamics
• A multifractal random walk
• Fractional calculus and continuous-time finance II: the waiting-time distribution
• Impact of non-Poisson activity patterns on spreading processes
• Statistical Properties of Share Volume Traded in Financial Markets
• Uncoupled continuous-time random walks: Solution and limiting behavior of the master equation
• A continuous time random walk model for financial distributions
• Exact results for the Barabasi model of human dynamics
• The continuous time random walk formalism in financial markets
• Scaling in the distribution of intertrade durations of Chinese stocks
• Entropy of the Nordic electricity market: anomalous scaling, spikes, and mean-reversion
• Modeling of waiting times and price changes in currency exchange data

Cited by in corpus (13)

• Multifractal analysis of financial markets
• Quantifying reflexivity in financial markets: towards a prediction of flash crashes
• Detrended fluctuation analysis made flexible to detect range of cross-correlated fluctuations
• The Continuous Time Random Walk, still trendy: Fifty-year history, state of art, and outlook
• Modeling scaled processes and 1/f^b noise by the nonlinear stochastic differential equations
• Dynamical variety of shapes in financial multifractality
• Universality of market superstatistics
• Universality and the collapse of multifractality in Barkhausen avalanches
• The new face of multifractality: Multi-branchedness and the phase transitions in time series of mean inter-event times
• Theory of earthquakes interevent times applied to financial markets
• Directed Continuous-Time Random Walk with memory
• Modeling non-stationarities in high-frequency financial time series
• Continuous-Time Random Walk with multi-step memory: An application to market dynamics