Return interval distribution of extreme events and long term memory

Abstract

The distribution of recurrence times or return intervals between extreme events is important to characterize and understand the behavior of physical systems and phenomena in many disciplines. It is well known that many physical processes in nature and society display long range correlations. Hence, in the last few years, considerable research effort has been directed towards studying the distribution of return intervals for long range correlated time series. Based on numerical simulations, it was shown that the return interval distributions are of stretched exponential type. In this paper, we obtain an analytical expression for the distribution of return intervals in long range correlated time series which holds good when the average return intervals are large. We show that the distribution is actually a product of power law and a stretched exponential form. We also discuss the regimes of validity and perform detailed studies on how the return interval distribution depends on the threshold used to define extreme events.

8 pages, 6 figures

References in corpus (14)

• Long-Term Clustering, Scaling, and Universality in the Temporal Occurrence of Earthquakes
• An integrated approach to the assessment of long range correlation in time series data
• Recurrence time analysis, long-term correlations, and extreme events
• "Universal" Distribution of Inter-Earthquake Times Explained
• Scaling and universality in rock fracture
• Scaling and memory of intraday volatility return intervals in stock market
• Universality in solar flare and earthquake occurrence
• Theory of Earthquake Recurrence Times
• The coronal mass ejection waiting-time distribution
• Scaling and correlations in the dynamics of forest-fire occurrence
• Extreme statistics of complex random and quantum chaotic states
• Nonlinear theory and tests of earthquake recurrence times
• Poincare recurrences from the perspective of transient chaos
• Universal Scaling Laws for Large Events in Driven Nonequilibrium Systems

Cited by in corpus (36)

• Beyond word frequency: Bursts, lulls, and scaling in the temporal distributions of words
• Extreme events in dynamical systems and random walkers: A review
• Extreme events on complex networks
• Effects of long memory in the order submission process on the properties of recurrence intervals of large price fluctuations
• Recurrence interval analysis of high-frequency financial returns and its application to risk estimation
• Extreme events in globally coupled chaotic maps
• Extreme value statistics and recurrence intervals of NYMEX energy futures volatility
• Scaling laws for diffusion on (trans)fractal scale-free networks
• Extreme events in a complex network: interplay between degree distribution and repulsive interaction
• Short term prediction of extreme returns based on the recurrence interval analysis
• Extreme value statistics and return intervals in long-range correlated uniform deviates
• Finite-Size Effects on Return Interval Distributions for Weakest-Link-Scaling Systems
• Scaling properties and universality of first-passage time probabilities in financial markets
• Persistence analysis of velocity and temperature fluctuations in convective surface layer turbulence
• Superstatistical analysis of sealevel fluctuations
• Extreme events in stochastic transport on networks
• Manipulation of extreme events on scale-free networks
• Extreme events in two dimensional disordered nonlinear lattices
• Copulas and time series with long-ranged dependences
• Fertility Heterogeneity as a Mechanism for Power Law Distributions of Recurrence Times
• Scaling and memory in the return intervals of energy dissipation rate in three-dimensional fully developed turbulence
• Extreme rotational events in a forced-damped nonlinear pendulum
• Long-term memory induced correction to Arrhenius law
• Universal patterns in sound amplitudes of songs and music genres
• Early warning of large volatilities based on recurrence interval analysis in Chinese stock markets
• Analysis of fluctuations in the first return times of random walks on regular branched networks
• Theory of earthquakes interevent times applied to financial markets
• Inferring long memory using extreme events
• Extreme Value Laws for Superstatistics
• The soundscape dynamics of human agglomeration
• On the dynamics of bubbles in boiling water
• Evacuation in the Social Force Model is not stationary
• Volatilities analysis of first-passage time and first-return time on a small-world scale-free network
• Analysis of inter-transaction time fluctuations in the cryptocurrency market
• Density of first Poincaré returns, periodic orbits, and Kolmogorov-Sinai entropy
• Extreme Events in Nonlinear Lattices