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Infinite ergodicity that preserves the Lebesgue measure.

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Flexible two-point selection approach for characteristic function-based parameter estimation of stable laws.

Shinji Kakinaka1, Ken Umeno1

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Summary
This summary is machine-generated.

We developed a new method for estimating stable distribution parameters using characteristic functions. This approach improves upon existing methods for modeling fat-tailed financial data.

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Area of Science:

  • Statistics
  • Financial Mathematics
  • Econometrics

Background:

  • Stable distributions are crucial for modeling fat-tailed phenomena and scaling in diverse scientific fields.
  • The method of moments offers a straightforward parameter estimation for stable laws but suffers from poorly defined point selection for characteristic functions.
  • Existing methods for stable law parameter estimation lack a comprehensive approach for selecting characteristic function points.

Purpose of the Study:

  • To introduce a novel characteristic function-based approach for stable distribution parameter estimation.
  • To enhance the practical applicability of the method of moments for stable laws.
  • To provide a robust method for modeling financial asset data with stable distributions.

Main Methods:

  • A new technique for selecting plausible points on the characteristic function is introduced.
  • The proposed method integrates this point selection technique into the method of moments framework.
  • The approach yields a closed-form expression for all four parameters of stable laws.

Main Results:

  • The new method outperforms current state-of-the-art techniques in estimating stable law parameters.
  • Numerical results demonstrate the method's advantage in modeling empirical financial data.
  • The approach provides a practical and accurate tool for stable distribution analysis.

Conclusions:

  • The proposed characteristic function-based method significantly advances stable distribution parameter estimation.
  • This technique makes the method of moments a more viable tool for practical applications.
  • The method is particularly effective for analyzing financial data exhibiting fat-tailed behaviors.