Ratio of Quantiles Indicates Burstiness with Fewer False Negatives than the Conventional Burstiness Parameter

TL;DR

The paper introduces the Burstiness Tail-based Index (BTI), a new metric that improves burstiness detection in time series data by reducing false negatives and increasing robustness over the traditional Burstiness Parameter (BP).

Contribution

The authors develop BTI, a quantile ratio-based metric that outperforms BP in classifying bursty distributions, especially with limited data or short observation periods.

Findings

BTI correctly classifies bursty distributions where BP fails.

BTI is more robust than BP with small sample sizes.

Applying BTI alters interpretations of burstiness in human activity data.

Abstract

Complexity researchers view burstiness--fluctuating levels of activity--as evidence of hidden interactions within the system generating the activity signal. Yet, current burstiness metrics miss evidence of burstiness in some moderately bursty distributions and under moderate sampling conditions. The canonical Burstiness Parameter (BP) compares distributions of timing statistics to the exponential distribution, representing the timing of independent random events, but it provides false negatives for some parameter ranges of power laws, with and without cut-offs. We introduce a metric that maintains BP's measurement approach but reduces false negatives: the Burstiness Tail-based Index (BTI). Based on ratios of differences in quantiles, BTI correctly classifies bursty distributions over certain parameter ranges misclassified by BP. Additionally, we find BTI to be more robust than BP in the presence of limited sample sizes and short observation windows, using simulated samples drawn from distributions correctly classified by BP in their analytical form. As a case study, we revisit an analysis of human activity data and find that the choice of BTI over BP influences interpretations of the timescales of burstiness in the dataset. Given these analytical, simulated, and empirical results, we argue for BTI's practical advantage over BP in assessing burstiness in real-world temporal signals for complexity research and time series modeling.