Self-Similar Extrapolation of Asymptotic Series and Forecasting for Time Series

Abstract

The method of extrapolating asymptotic series, based on the Self-Similar Approximation Theory, is developed. Several important questions are answered, which makes the foundation of the method unambiguous and its application straightforward. It is shown how the extrapolation of asymptotic series can be reformulated as forecasting for time series. The probability measure is introduced characterizing the ensemble of forecasted scenarios. The way of choosing the complete family of data bases is advanced.

LaTex, 11 pages

Cited by in corpus (9)

• Self-Similar Factor Approximants
• Summation of Power Series by Self-Similar Factor Approximants
• Self-Similar Structures and Fractal Transforms in Approximation Theory
• Extrapolation of power series by self-similar factor and root approximants
• Self-Similar Law of Energy Release before Materials Fracture
• Interplay Between Approximation Theory and Renormalization Group
• Expansion Exponents for Nonequilibrium Systems
• Non-perturbative calculations for the effective potential of the $PT$ symmetric and non-Hermitian $(-g{\varphi }^4)$ field theoretic model
• Self-Similar Extrapolation for the Law of Acoustic Emission Before Failure of Heterogeneous Materials