Least-Squares Estimators of Drift Parameter for Discretely Observed Fractional Ornstein–Uhlenbeck Processes
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 thei...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/5/716 |
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| author | Pavel Kříž Leszek Szała |
| author_facet | Pavel Kříž Leszek Szała |
| author_sort | Pavel Kříž |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T20:03:58Z |
| format | Article |
| id | doaj.art-e17828fcc7a24e4d8cad7cd07b955d98 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T20:03:58Z |
| publishDate | 2020-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-e17828fcc7a24e4d8cad7cd07b955d982023-11-19T23:25:02ZengMDPI AGMathematics2227-73902020-05-018571610.3390/math8050716Least-Squares Estimators of Drift Parameter for Discretely Observed Fractional Ornstein–Uhlenbeck ProcessesPavel Kříž0Leszek Szała1Department of Mathematics, Faculty of Chemical Engineering, University of Chemistry and Technology Prague, 16628 Prague, Czech RepublicDepartment of Mathematics, Faculty of Chemical Engineering, University of Chemistry and Technology Prague, 16628 Prague, Czech RepublicWe 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.https://www.mdpi.com/2227-7390/8/5/716fractional Brownian motionOrnstein–Uhlenbeck processdrift parameter estimation |
| spellingShingle | Pavel Kříž Leszek Szała Least-Squares Estimators of Drift Parameter for Discretely Observed Fractional Ornstein–Uhlenbeck Processes Mathematics fractional Brownian motion Ornstein–Uhlenbeck process drift parameter estimation |
| title | Least-Squares Estimators of Drift Parameter for Discretely Observed Fractional Ornstein–Uhlenbeck Processes |
| title_full | Least-Squares Estimators of Drift Parameter for Discretely Observed Fractional Ornstein–Uhlenbeck Processes |
| title_fullStr | Least-Squares Estimators of Drift Parameter for Discretely Observed Fractional Ornstein–Uhlenbeck Processes |
| title_full_unstemmed | Least-Squares Estimators of Drift Parameter for Discretely Observed Fractional Ornstein–Uhlenbeck Processes |
| title_short | Least-Squares Estimators of Drift Parameter for Discretely Observed Fractional Ornstein–Uhlenbeck Processes |
| title_sort | least squares estimators of drift parameter for discretely observed fractional ornstein uhlenbeck processes |
| topic | fractional Brownian motion Ornstein–Uhlenbeck process drift parameter estimation |
| url | https://www.mdpi.com/2227-7390/8/5/716 |
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