Inferring long memory using extreme events
arXiv:2011.11018 · doi:10.1063/5.0064432
Abstract
Many natural and physical processes display long memory and extreme events. In these systems, the measured time series is invariably contaminated by noise. As the extreme events display large deviation from the mean behaviour, the noise does 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, they can be used to infer the correlation properties of the latter. In this work, from a given time series, we construct three modified time series using only the extreme events. It is shown that the correlations in the original time series and in the modified time series, as measured by the exponent obtained from detrended fluctuation analysis technique, are related to each other. Hence, the correlation exponents for a long memory time series can be inferred from its extreme events alone. This approach is demonstrated for several empirical time series.
9 pages, 7 figures
References in corpus (7)
- Comparison of detrending methods for fluctuation analysis
- Recurrence time analysis, long-term correlations, and extreme events
- Effect of extreme data loss on long-range correlated and anti-correlated signals quantified by detrended fluctuation analysis
- Return interval distribution of extreme events and long term memory
- Theoretical foundation of detrending methods for fluctuation analysis such as detrended fluctuation analysis and detrending moving average
- Quantum spectrum as a time series : Fluctuation measures
- Probabilistic properties of detrended fluctuation analysis for Gaussian processes