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Levy scaling in random walks with fluctuating variance

Santini1

  • 1Institute of Theoretical Physics, University of Lausanne, CH-1015 Lausanne, Switzerland.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|October 25, 2000
PubMed
Summary

This study introduces a model for truncated Levy flights with fluctuating variance. It shows that correlated variance fluctuations can delay the transition to a Gaussian distribution, impacting economic time series analysis.

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Area of Science:

  • Stochastic processes
  • Time series analysis
  • Statistical modeling

Background:

  • Conventional truncated Levy flights assume fixed variance.
  • Heteroskedasticity, or fluctuating variance, is common in financial data.
  • Understanding these fluctuations is key to accurate modeling.

Purpose of the Study:

  • To introduce a stylized model for truncated Levy flights with heteroskedasticity.
  • To analyze the impact of correlated variance fluctuations on the probability distribution.
  • To explore potential applications in economic time series.

Main Methods:

  • Development of a stylized model where variance follows a two-state Markov chain.
  • Analysis of the probability distribution function (PDF) of increments.

Related Experiment Videos

  • Comparison with conventional truncated Levy flights.

    • Main Results:

    • The central part of the PDF remains Levy-like at short timescales.
    • Correlated variance fluctuations significantly delay the crossover to the Gaussian regime.
    • The observed behavior differs from processes with uncorrelated variance.

    Conclusions:

    • The proposed model captures essential features of Levy scaling with heteroskedasticity.
    • This approach offers a more realistic framework for modeling certain economic time series.
    • The findings have implications for understanding complex financial dynamics.