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Iterated function system models in data analysis: detection and separation.

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  • 1Applied Mathematics, University of Colorado, Boulder, Colorado 80309-0526, USA. alexanz@colorado.edu

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This study introduces a new algorithm for analyzing iterated function systems (IFS) data. The method accurately detects regime switches in time series, offering applications in data analysis and digital communications.

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Area of Science:

  • Dynamical Systems
  • Data Analysis
  • Time Series Analysis

Background:

  • Iterated Function Systems (IFS) are discrete-time dynamical systems.
  • These systems involve a finite set of maps representing distinct dynamical regimes.
  • Regime switches can occur deterministically or stochastically.

Purpose of the Study:

  • To develop an algorithm for detecting regime switches in time series data generated by IFS models.
  • To validate the algorithm's performance on sample datasets.

Main Methods:

  • The algorithm assumes continuity of the maps within the IFS.
  • It processes time series data to identify sequences of regime switches.
  • The method was tested on a basic example and a computer performance dataset.

Main Results:

  • The algorithm successfully detected regime switches in the tested datasets.
  • Demonstrated the feasibility of the proposed methodology for IFS data analysis.

Conclusions:

  • The developed algorithm provides an effective approach for regime switch detection in IFS.
  • This methodology has broad applicability, including change-point detection and digital communications.