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

摘要

A record is an entry in a time series that is larger or smaller than allprevious entries. If the time series consists of independent, identicallydistributed random variables with a superimposed linear trend, record eventsare positively (negatively) correlated when the tail of the distribution isheavier (lighter) than exponential. Here we use these correlations to detectheavy-tailed behavior in small sets of independent random variables. The methodconsists of converting random subsets of the data into time series with atunable linear drift and computing the resulting record correlations.