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Measure of predictability.

Weiguang Yao1, Christopher Essex, Pei Yu

  • 1Applied Mathematics Department, University of Western Ontario, London, Ontario, Canada N6A 5B7. wgyao@uwo.ca

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 13, 2004
PubMed
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This study introduces forecast entropy, a new measure for time series predictability. It quantizes how predictable a time series is, aiding in analyzing chaotic and random systems.

Area of Science:

  • * Data Science
  • * Chaos Theory
  • * Time Series Analysis

Background:

  • * Existing methods for measuring time series forecasting difficulty are numerous.
  • * Quantifying the inherent predictability of time series data remains a challenge.

Purpose of the Study:

  • * To introduce a novel measure, forecast entropy, for quantifying time series predictability.
  • * To establish a standardized method for assessing the predictability of time series data.

Main Methods:

  • * Reconstructing attractors from time series data.
  • * Analyzing data distributions in regular and tangent spaces across different scales.
  • * Developing a formula for calculating forecast entropy.
  • * Defining an idealized random system for normalization.

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Main Results:

  • * Forecast entropy successfully measures the predictability of time series.
  • * The measure distinguishes between chaotic and pseudorandom systems.
  • * Forecast entropy aids in selecting optimal parameters for attractor reconstruction.

Conclusions:

  • * Forecast entropy provides a robust tool for time series predictability assessment.
  • * The method offers insights into the underlying dynamics of deterministic and random systems.
  • * This measure can optimize attractor reconstruction for improved time series analysis.