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Least-Squares Estimators of Drift Parameter for Discretely Observed Fractional Ornstein–Uhlenbeck Processes

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  • Pavel Kříž

    (Department of Mathematics, Faculty of Chemical Engineering, University of Chemistry and Technology Prague, 16628 Prague, Czech Republic)

  • Leszek Szała

    (Department of Mathematics, Faculty of Chemical Engineering, University of Chemistry and Technology Prague, 16628 Prague, Czech Republic)

Abstract

We introduce three new estimators of the drift parameter of a fractional Ornstein–Uhlenbeck process. These estimators are based on modifications of the least-squares procedure utilizing the explicit formula for the process and covariance structure of a fractional Brownian motion. We demonstrate their advantageous properties in the setting of discrete-time observations with fixed mesh size, where they outperform the existing estimators. Numerical experiments by Monte Carlo simulations are conducted to confirm and illustrate theoretical findings. New estimation techniques can improve calibration of models in the form of linear stochastic differential equations driven by a fractional Brownian motion, which are used in diverse fields such as biology, neuroscience, finance and many others.

Suggested Citation

  • Pavel Kříž & Leszek Szała, 2020. "Least-Squares Estimators of Drift Parameter for Discretely Observed Fractional Ornstein–Uhlenbeck Processes," Mathematics, MDPI, vol. 8(5), pages 1-20, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:716-:d:353646
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    References listed on IDEAS

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