Inferring long memory using extreme events.

Abstract

Many natural and physical processes display long memory and extreme events. In these systems, the measured time series is invariably contaminated by noise and/or missing data. As the extreme events display a large deviation from the mean behavior, noise and/or missing data do not affect the extreme events as much as it affects the typical values. Since the extreme events also carry the information about correlations in the full-time series, we can use them to infer the correlation properties of the latter. In this work, we construct three modified time series using only the extreme events from a given time series. We show that the correlations in the original time series and in the modified time series are related, as measured by the exponent obtained from the detrended fluctuation analysis technique. Hence, the correlation exponents for a long memory time series can be inferred from its extreme events alone. We demonstrate this approach for several empirical time series.