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A least square-type procedure for parameter estimation in stochastic differential equations with additive fractional noise

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  • Andreas Neuenkirch
  • Samy Tindel

Abstract

We study a least square-type estimator for an unknown parameter in the drift coefficient of a stochastic differential equation with additive fractional noise of Hurst parameter $$H>1/2$$ H > 1 / 2 . The estimator is based on discrete time observations of the stochastic differential equation, and using tools from ergodic theory and stochastic analysis we derive its strong consistency. Copyright Springer Science+Business Media Dordrecht 2014

Suggested Citation

  • Andreas Neuenkirch & Samy Tindel, 2014. "A least square-type procedure for parameter estimation in stochastic differential equations with additive fractional noise," Statistical Inference for Stochastic Processes, Springer, vol. 17(1), pages 99-120, April.
    • Handle: RePEc:spr:sistpr:v:17:y:2014:i:1:p:99-120
    DOI: 10.1007/s11203-013-9084-z
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    References listed on IDEAS

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    1. Kasonga, R. A., 1988. "The consistency of a non-linear least squares estimator from diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 30(2), pages 263-275, December.
    2. Christian Bender & Tommi Sottinen & Esko Valkeila, 2008. "Pricing by hedging and no-arbitrage beyond semimartingales," Finance and Stochastics, Springer, vol. 12(4), pages 441-468, October.
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    5. Frydman, Roman, 1980. "A Proof of the Consistency of Maximum Likelihood Estimators of Nonlinear Regression Models with Autocorrelated Errors," Econometrica, Econometric Society, vol. 48(4), pages 853-860, May.
    6. Hu, Yaozhong & Nualart, David, 2010. "Parameter estimation for fractional Ornstein-Uhlenbeck processes," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 1030-1038, June.
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    Citations

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    Cited by:

    1. Liu, Yanghui & Nualart, Eulalia & Tindel, Samy, 2019. "LAN property for stochastic differential equations with additive fractional noise and continuous time observation," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2880-2902.
    2. Fabienne Comte & Nicolas Marie, 2019. "Nonparametric estimation in fractional SDE," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 359-382, October.
    3. Es-Sebaiy, Khalifa & Viens, Frederi G., 2019. "Optimal rates for parameter estimation of stationary Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3018-3054.
    4. Marie, Nicolas, 2020. "Nonparametric estimation of the trend in reflected fractional SDE," Statistics & Probability Letters, Elsevier, vol. 158(C).
    5. Fabienne Comte & Nicolas Marie, 2021. "Nonparametric estimation for I.I.D. paths of fractional SDE," Statistical Inference for Stochastic Processes, Springer, vol. 24(3), pages 669-705, October.
    6. Marie, Nicolas, 2022. "Projection estimators of the stationary density of a differential equation driven by the fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 180(C).
    7. Li, Yicun & Teng, Yuanyang, 2023. "Statistical inference in discretely observed fractional Ornstein–Uhlenbeck processes," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    8. Kohei Chiba, 2020. "An M-estimator for stochastic differential equations driven by fractional Brownian motion with small Hurst parameter," Statistical Inference for Stochastic Processes, Springer, vol. 23(2), pages 319-353, July.
    9. Nakajima, Shohei & Shimizu, Yasutaka, 2022. "Asymptotic normality of least squares type estimators to stochastic differential equations driven by fractional Brownian motions," Statistics & Probability Letters, Elsevier, vol. 187(C).
    10. 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.

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