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Bayesian inference for fractional Oscillating Brownian motion

Author

Listed:
  • Héctor Araya

    (Universidad de Valparaíso)

  • Meryem Slaoui

    (Université de Lille)

  • Soledad Torres

    (Universidad de Valparaíso)

Abstract

This paper deals with the problem of parameter estimation in a class of stochastic differential equations driven by a fractional Brownian motion with $$H \ge 1/2$$ H ≥ 1 / 2 and a discontinuous coefficient in the diffusion. Two Bayesian type estimators are proposed for the diffusion parameters based on Markov Chain Monte Carlo and Approximate Bayesian Computation methods.

Suggested Citation

  • Héctor Araya & Meryem Slaoui & Soledad Torres, 2022. "Bayesian inference for fractional Oscillating Brownian motion," Computational Statistics, Springer, vol. 37(2), pages 887-907, April.
    • Handle: RePEc:spr:compst:v:37:y:2022:i:2:d:10.1007_s00180-021-01146-8
    DOI: 10.1007/s00180-021-01146-8
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    References listed on IDEAS

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    1. Antoine Lejay & Paolo Pigato, 2019. "A Threshold Model For Local Volatility: Evidence Of Leverage And Mean Reversion Effects On Historical Data," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1-24, June.
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    4. Pauliina Ilmonen & Soledad Torres & Lauri Viitasaari, 2020. "Oscillating Gaussian processes," Statistical Inference for Stochastic Processes, Springer, vol. 23(3), pages 571-593, October.
    5. Tommi Sottinen, 2001. "Fractional Brownian motion, random walks and binary market models," Finance and Stochastics, Springer, vol. 5(3), pages 343-355.
    6. Ajay Jasra, 2015. "Approximate Bayesian Computation for a Class of Time Series Models," International Statistical Review, International Statistical Institute, vol. 83(3), pages 405-435, December.
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