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A model-free characterization of recurrences in stationary time series

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  • R\'emy Chicheportiche
  • Anirban Chakraborti
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    Abstract

    Study of recurrences in earthquakes, climate, financial time-series, etc. is crucial to better forecast disasters and limit their consequences. However, almost all the previous phenomenological studies involved only a long-ranged autocorrelation function, or disregarded the multi-scaling properties induced by potential higher order dependencies. Consequently, they missed the facts that non-linear dependences do impact both the statistics and dynamics of recurrence times, and that scaling arguments for the unconditional distribution may not be applicable. We argue that copulas is the correct model-free framework to study non-linear dependencies in time series and related concepts like recurrences. Fitting and/or simulating the intertemporal distribution of recurrence intervals is very much system specific, and cannot actually benefit from universal features, in contrast to the previous claims. This has important implications in epilepsy prognosis and financial risk management applications.

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    File URL: http://arxiv.org/pdf/1302.3704
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1302.3704.

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    Date of creation: Feb 2013
    Date of revision: Sep 2013
    Handle: RePEc:arx:papers:1302.3704

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    Web page: http://arxiv.org/

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