Measuring burstiness for finite event sequences

TL;DR

This paper investigates the limitations of the existing burstiness measure in finite event sequences, analytically characterizes finite-size effects, and proposes a new, robust measure to better capture intrinsic bursty behavior in empirical data.

Contribution

The authors analytically examine finite-size effects on the burstiness parameter and introduce a new measure that accurately reflects intrinsic burstiness regardless of sequence length.

Findings

Finite-size effects significantly distort the traditional burstiness measure.

The new burstiness measure is unaffected by the number of events in the sequence.

Empirical data analysis demonstrates the robustness of the proposed measure.

Abstract

Characterizing inhomogeneous temporal patterns in natural and social phenomena is important to understand underlying mechanisms behind such complex systems, hence even to predict and control them. Temporal inhomogeneities in event sequences have been described in terms of bursts that are rapidly occurring events in short time periods alternating with long inactive periods. The bursts can be quantified by a simple measure, called burstiness parameter, which was introduced by Goh and Barab\'asi [EPL \textbf{81}, 48002 (2008)]. The burstiness parameter has been widely used due to its simplicity, which however turns out to be strongly affected by the finite number of events in the time series. As the finite-size effects on burstiness parameter have been largely ignored, we analytically investigate the finite-size effects of the burstiness parameter. Then we suggest an alternative definition of burstiness that is free from finite-size effects and yet simple. Using our alternative burstiness measure, one can distinguish the finite-size effects from the intrinsic bursty properties in the time series. We also demonstrate the advantages of our burstiness measure by analyzing empirical datasets.