Statistics of Extreme Values in Time Series with Intermediate-Term Correlations

Abstract

It will be discussed the statistics of the extreme values in time series characterized by finite-term correlations with non-exponential decay. Precisely, it will be considered the results of numerical analyses concerning the return intervals of extreme values of the fluctuations of resistance and defect-fraction displayed by a resistor with granular structure in a nonequilibrium stationary state. The resistance and defect-fraction are calculated as a function of time by Monte Carlo simulations using a resistor network approach. It will be shown that when the auto-correlation function of the fluctuations displays a non-exponential and non-power-law decay, the distribution of the return intervals of extreme values is a stretched exponential, with exponent largely independent of the threshold. Recently, a stretched exponential distribution of the return intervals of extreme values has been identified in long-term correlated time series by Bunde et al. (2003) and Altmann and Kantz (2005). Thus, the present results show that the stretched exponential distribution of the return intervals is not an exclusive feature of long-term correlated time series.

6 pages, 7 figures, conference paper, in Noise and Stochastics in Complex Systems and Finance, ed. by J. Kertez, S. Bornhold, R. N. Mantegna, Procs. of SPIE, vol. 6601, 19, 2007

References in corpus (14)

• Unified Scaling Law for Earthquakes
• Long-Term Clustering, Scaling, and Universality in the Temporal Occurrence of Earthquakes
• Method for Generating Long-Range Correlations for Large Systems
• Magnitude and Sign Correlations in Heartbeat Fluctuations
• Power Laws in Solar Flares: Self-Organized Criticality or Turbulence?
• Correlations in Economic Time Series
• Recurrence time analysis, long-term correlations, and extreme events
• 1/f Noise and Extreme Value Statistics
• Simple model for 1/f noise
• A Biased Resistor Network Model for Electromigration Failure and Related Phenomena in Metallic Lines
• Resistance and Resistance Fluctuations in Random Resistor Networks Under Biased Percolation
• Non-Gaussian Resistance Noise near Electrical Breakdown in Granular Materials
• Distribution of Return Intervals of Extreme Events
• Long-term Correlations and 1/f^alpha Noise in the Steady States of Multi-Species Resistor Networks