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Time Series Complexities and Their Relationship to Forecasting Performance.

Mirna Ponce-Flores1, Juan Frausto-Solís1, Guillermo Santamaría-Bonfil2

  • 1Graduate Program Division, Tecnológico Nacional de México/Instituto Tecnológico de Ciudad Madero, Cd. Madero 89440, Mexico.

Entropy (Basel, Switzerland)
|December 8, 2020
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Summary
This summary is machine-generated.

This study links time series complexity measures, like Spectral Entropy, to forecasting errors. It helps predict which forecasting methods (ARIMA, ETS, etc.) will perform best based on signal complexity.

Keywords:
M4 competitionclassical forecasting methodscomplexityentropyerror measuressymbolic analysis

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Area of Science:

  • Time Series Analysis
  • Information Theory
  • Computational Statistics

Background:

  • Entropy measures signal uncertainty and time series complexity.
  • Spectral Entropy and Permutation Entropy are common complexity metrics.
  • Discretization in complexity measures affects their reliability.

Purpose of the Study:

  • To establish the relationship between entropy-based complexity and forecasting errors.
  • To identify optimal forecasting methods for different time series complexities.
  • To extend complexity frameworks using the Emergence, Self-Organization, and Complexity paradigm.

Main Methods:

  • Utilized Spectral Entropy and Permutation Entropy for complexity assessment.
  • Analyzed forecasting errors of Smyl, Theta, ARIMA, and ETS methods.
  • Experimented with synthetic and M4 Competition time series data.
  • Developed an extended complexity framework based on Emergence, Self-Organization, and Complexity.

Main Results:

  • A clear relationship was found between complexity measures and forecasting errors.
  • The feature space of complexity metrics visually constrains forecasting method performance.
  • Higher complexity, particularly based on emergence and self-organization, correlated with poorer logarithmic metric error.

Conclusions:

  • Complexity measures can predict forecasting method performance.
  • The proposed extended framework offers insights into time series behavior.
  • This approach aids in selecting appropriate forecasting algorithms in advance.