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Two approaches to consistent estimation of parameters of mixed fractional Brownian motion with trend

Author

Listed:
  • Alexander Kukush

    (Taras Shevchenko National University of Kyiv)

  • Stanislav Lohvinenko

    (Taras Shevchenko National University of Kyiv)

  • Yuliya Mishura

    (Taras Shevchenko National University of Kyiv)

  • Kostiantyn Ralchenko

    (Taras Shevchenko National University of Kyiv)

Abstract

We investigate the mixed fractional Brownian motion with trend of the form $$X_t = \theta t + \sigma W_t + \kappa B^H_t$$ X t = θ t + σ W t + κ B t H , driven by a standard Brownian motion W and a fractional Brownian motion $$B^H$$ B H with Hurst parameter H. We develop and compare two approaches to estimation of four unknown parameters $$\theta $$ θ , $$\sigma $$ σ , $$\kappa $$ κ and H by discrete observations. The first algorithm is more traditional: we estimate $$\sigma $$ σ , $$\kappa $$ κ and H using the quadratic variations, while the estimator of $$\theta $$ θ is obtained as a discretization of a continuous-time estimator of maximum likelihood type. This approach has several limitations, in particular, it assumes that $$H

Suggested Citation

  • Alexander Kukush & Stanislav Lohvinenko & Yuliya Mishura & Kostiantyn Ralchenko, 2022. "Two approaches to consistent estimation of parameters of mixed fractional Brownian motion with trend," Statistical Inference for Stochastic Processes, Springer, vol. 25(1), pages 159-187, April.
    • Handle: RePEc:spr:sistpr:v:25:y:2022:i:1:d:10.1007_s11203-021-09252-6
    DOI: 10.1007/s11203-021-09252-6
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    References listed on IDEAS

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