# Copula-based algorithm for generating bursty time series

## TL;DR

This paper introduces a copula-based algorithm to generate bursty time series with correlated interevent times, capturing non-Poissonian patterns and memory effects for more realistic modeling of dynamical processes.

## Contribution

A novel copula-based method for generating correlated, heavy-tailed bursty time series, outperforming existing shuffling techniques in certain scenarios.

## Key findings

- Successfully generates event sequences with heavy-tailed IET distributions.
- Outperforms shuffling method in specific cases.
- Applicable to modeling diverse dynamical processes.

## Abstract

Dynamical processes in various natural and social phenomena have been described by a series of events or event sequences showing non-Poissonian, bursty temporal patterns. Temporal correlations in such bursty time series can be understood not only by heterogeneous interevent times (IETs) but also by correlations between IETs. Modeling and simulating various dynamical processes requires us to generate event sequences with a heavy-tailed IET distribution and memory effects between IETs. For this, we propose a Farlie-Gumbel-Morgenstern copula-based algorithm for generating event sequences with correlated IETs when the IET distribution and the memory coefficient between two consecutive IETs are given. We successfully apply our algorithm to the cases with heavy-tailed IET distributions. We also compare our algorithm to the existing shuffling method to find that our algorithm outperforms the shuffling method for some cases. Our copula-based algorithm is expected to be used for more realistic modeling of various dynamical processes.