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Geophysical Monograph Series



  • extreme events
  • long memory
  • recurrence
  • return intervals
  • earthquakes
  • recurrence statistics

Index Terms

  • 3235 Mathematical Geophysics: Persistence, memory, correlations, clustering
  • 4313 Natural Hazards: Extreme events
  • 4430 Nonlinear Geophysics: Complex systems
  • 3265 Mathematical Geophysics: Stochastic processes



Extreme Event Recurrence Time Distributions and Long Memory

M. S. Santhanam

Indian Institute of Science Education and Research, Pune, India

The distribution of return intervals for extreme events is an important quantity of interest in many fields ranging from physics and geophysical sciences to finance and physiology. Extreme events are understood to imply exceedance of a discretely sampled time series above a prescribed threshold q. The recurrence or return interval is the elapsed time interval between successive extreme events. The question is if it is possible to determine the recurrence or return interval distribution from the knowledge of the temporal dependencies in a time series. The return interval distribution for uncorrelated time series is known to have an exponentially decaying form. What is the behavior of return interval distribution for processes that display long memory? This question assumes importance because most of the naturally occurring physical processes display long-memory property. Long memory implies slow decay of autocorrelations. In recent times, considerable research effort has been directed toward studying the distribution of return intervals for such time series. In this chapter, we review the work done in this area in the last few years and discuss the results arising from simulations as well as from analytical approaches while paying special attention to the recent developments in the recurrence time statistics for seismic activity. We also point out many parallel results in areas ranging from computing to finance.

Citation: Santhanam, M. S. (2012), Extreme event recurrence time distributions and long memory, in Extreme Events and Natural Hazards: The Complexity Perspective, Geophys. Monogr. Ser., vol. 196, edited by A. S. Sharma et al. 335–344, AGU, Washington, D. C., doi:10.1029/2011GM001145.


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