Correlations of record events as a test for heavy-tailed distributions

TL;DR

This paper introduces a method to detect heavy-tailed distributions by analyzing correlations of record events in time series with a linear trend, useful for small datasets.

Contribution

It proposes a novel approach using record correlations in trending time series to identify heavy-tailed behavior in small independent datasets.

Findings

Record correlations are positive for heavy tails and negative for light tails.

The method effectively detects heavy-tailed distributions in small data samples.

Correlation analysis provides a new diagnostic tool for distribution tail behavior.

Abstract

A record is an entry in a time series that is larger or smaller than all previous entries. If the time series consists of independent, identically distributed random variables with a superimposed linear trend, record events are positively (negatively) correlated when the tail of the distribution is heavier (lighter) than exponential. Here we use these correlations to detect heavy-tailed behavior in small sets of independent random variables. The method consists of converting random subsets of the data into time series with a tunable linear drift and computing the resulting record correlations.