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Bayesian inference for the log-symmetric autoregressive conditional duration model.

Jeremias Leão1, Rafael Paixão2, Helton Saulo3

  • 1Departamento de Estatística, Universidade Federal do Amazonas, Campus Senador Arthur Virgílio Filho, Av. General Rodrigo Octávio, 6200, Coronado I, 69080-900 Manaus, AM, Brazil.

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This study introduces Hamiltonian Monte Carlo methods for log-symmetric autoregressive conditional duration models, enabling flexible modeling of duration time distributions. The Bayesian approach proved effective for parameter estimation and model performance evaluation.

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Area of Science:

  • Statistics
  • Econometrics
  • Computational Finance

Background:

  • Autoregressive conditional duration models are crucial for analyzing time-to-event data.
  • Log-symmetric distributions offer flexibility in modeling duration time, including median and skewness.
  • Efficient parameter estimation methods are needed for these advanced duration models.

Purpose of the Study:

  • To adapt Hamiltonian Monte Carlo (HMC) methods for log-symmetric autoregressive conditional duration models.
  • To employ a Bayesian approach for estimating model parameters.
  • To evaluate the performance of the proposed estimation methodology.

Main Methods:

  • Adaptation of Hamiltonian Monte Carlo (HMC) algorithms.
  • Bayesian inference for parameter estimation.
  • Monte Carlo simulation studies for performance evaluation.
  • Application to high-frequency financial data (German DAX 2016).

Main Results:

  • Successful adaptation of HMC methods for log-symmetric duration models.
  • Demonstration of the Bayesian approach's effectiveness in parameter estimation.
  • Validation of the methodology through simulation and real-world financial data analysis.

Conclusions:

  • The proposed Bayesian estimation methodology using HMC is suitable for log-symmetric autoregressive conditional duration models.
  • The approach provides a robust framework for analyzing financial duration data.
  • This work enhances the toolkit for modeling complex temporal dependencies in financial markets.