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Approximated maximum likelihood estimation in multifractal random walks.

O Løvsletten1, M Rypdal

  • 1Department of Mathematics and Statistics, University of Tromsø, 9037 Tromsø, Norway. ola.lovsletten@uit.no

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 12, 2012
PubMed
Summary
This summary is machine-generated.

We developed a new method to analyze multifractal random walk (MRW) processes, improving parameter estimation for financial markets. This approach offers a robust tool for understanding complex financial dynamics.

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Area of Science:

  • Quantitative Finance
  • Statistical Physics
  • Computational Economics

Background:

  • Multifractal random walk (MRW) models capture complex dynamics in financial time series.
  • Accurate parameter estimation is crucial for understanding and predicting market behavior.
  • Existing methods may face challenges with the inherent complexity of MRW processes.

Purpose of the Study:

  • To introduce an approximated maximum likelihood method for MRW processes.
  • To provide an efficient computational tool for MRW parameter estimation.
  • To evaluate the performance of the new method against existing techniques.

Main Methods:

  • Utilized Laplace approximation for likelihood computation.
  • Implemented a truncation in the dependency structure of latent volatility.
  • Developed an R package for practical application.
  • Compared performance against the generalized method of moments (GMM).

Main Results:

  • The approximated maximum likelihood method demonstrates effective parameter estimation for MRW processes.
  • Performance was validated using synthetic data.
  • The method was successfully applied to estimate parameters for real-world financial stock indices.
  • Results show competitive or improved performance compared to GMM.

Conclusions:

  • The proposed approximated maximum likelihood method offers a viable and efficient approach for analyzing MRW processes.
  • The R package facilitates the application of this method in financial research.
  • This tool enhances the ability to model and understand complex financial market dynamics.