IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v51y2024i3p1181-1205.html
   My bibliography  Save this article

Efficient drift parameter estimation for ergodic solutions of backward SDEs

Author

Listed:
  • Teppei Ogihara
  • Mitja Stadje

Abstract

We derive consistency and asymptotic normality results for quasi‐maximum likelihood methods for drift parameters of ergodic stochastic processes observed in discrete time in an underlying continuous‐time setting. The special feature of our analysis is that the stochastic integral part is unobserved and nonparametric. Additionally, the drift may depend on the (unknown and unobserved) stochastic integrand. Our results hold for ergodic semi‐parametric diffusions and backward SDEs. Simulation studies confirm that the methods proposed yield good convergence results.

Suggested Citation

  • Teppei Ogihara & Mitja Stadje, 2024. "Efficient drift parameter estimation for ergodic solutions of backward SDEs," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(3), pages 1181-1205, September.
    • Handle: RePEc:bla:scjsta:v:51:y:2024:i:3:p:1181-1205
    DOI: 10.1111/sjos.12709
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/sjos.12709
    Download Restriction: no
    File URL: https://libkey.io/10.1111/sjos.12709?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Nakahiro Yoshida, 2011. "Polynomial type large deviation inequalities and quasi-likelihood analysis for stochastic differential equations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(3), pages 431-479, June.
    2. Richou, Adrien, 2009. "Ergodic BSDEs and related PDEs with Neumann boundary conditions," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2945-2969, September.
    3. Wing Fung Chong & Ying Hu & Gechun Liang & Thaleia Zariphopoulou, 2019. "An ergodic BSDE approach to forward entropic risk measures: representation and large-maturity behavior," Finance and Stochastics, Springer, vol. 23(1), pages 239-273, January.
    4. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    5. Ying Hu & Gechun Liang & Shanjian Tang, 2018. "Systems of ergodic BSDEs arising in regime switching forward performance processes," Papers 1807.01816, arXiv.org, revised Jun 2020.
    6. Veretennikov, A. Yu., 1997. "On polynomial mixing bounds for stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 70(1), pages 115-127, October.
    7. Yoshida, Nakahiro, 1992. "Estimation for diffusion processes from discrete observation," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 220-242, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kou Fujimori, 2019. "The Dantzig selector for a linear model of diffusion processes," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 475-498, October.
    2. Chong, Wing Fung, 2019. "Pricing and hedging equity-linked life insurance contracts beyond the classical paradigm: The principle of equivalent forward preferences," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 93-107.
    3. Haruhiko Inatsugu & Nakahiro Yoshida, 2021. "Global jump filters and quasi-likelihood analysis for volatility," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 555-598, June.
    4. Debussche, Arnaud & Hu, Ying & Tessitore, Gianmario, 2011. "Ergodic BSDEs under weak dissipative assumptions," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 407-426, March.
    5. Nakahiro Yoshida, 2022. "Quasi-likelihood analysis and its applications," Statistical Inference for Stochastic Processes, Springer, vol. 25(1), pages 43-60, April.
    6. Gechun Liang & Yifan Sun & Thaleia Zariphopoulou, 2023. "Representation of forward performance criteria with random endowment via FBSDE and application to forward optimized certainty equivalent," Papers 2401.00103, arXiv.org.
    7. Masahiro Kurisaki, 2023. "Parameter estimation for ergodic linear SDEs from partial and discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 26(2), pages 279-330, July.
    8. Ogihara, Teppei & Yoshida, Nakahiro, 2014. "Quasi-likelihood analysis for nonsynchronously observed diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 2954-3008.
    9. Kengo Kamatani & Masayuki Uchida, 2015. "Hybrid multi-step estimators for stochastic differential equations based on sampled data," Statistical Inference for Stochastic Processes, Springer, vol. 18(2), pages 177-204, July.
    10. Shoichi Eguchi & Hiroki Masuda, 2019. "Data driven time scale in Gaussian quasi-likelihood inference," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 383-430, October.
    11. Alessandro Gregorio & Francesco Iafrate, 2021. "Regularized bridge-type estimation with multiple penalties," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(5), pages 921-951, October.
    12. Shogo Kusano & Masayuki Uchida, 2025. "Quasi-Bayesian information criterion of SEM for diffusion processes based on high-frequency data," Statistical Inference for Stochastic Processes, Springer, vol. 28(2), pages 1-28, August.
    13. Papanicolaou, Alex & Giesecke, Kay, 2016. "Variation-based tests for volatility misspecification," Journal of Econometrics, Elsevier, vol. 191(1), pages 217-230.
    14. Wing Fung Chong & Gechun Liang, 2024. "Robust forward investment and consumption under drift and volatility uncertainties: A randomization approach," Papers 2410.01378, arXiv.org.
    15. Yusuke Kaino & Masayuki Uchida, 2018. "Hybrid estimators for small diffusion processes based on reduced data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(7), pages 745-773, October.
    16. Yoshida, Nakahiro, 2025. "Quasi-likelihood analysis for nonlinear stochastic processes," Econometrics and Statistics, Elsevier, vol. 33(C), pages 246-257.
    17. Sangyeol Lee & Hiroki Masuda, 2010. "Jarque–Bera normality test for the driving Lévy process of a discretely observed univariate SDE," Statistical Inference for Stochastic Processes, Springer, vol. 13(2), pages 147-161, June.
    18. A. Gregorio & S. M. Iacus, 2019. "Empirical $$L^2$$ L 2 -distance test statistics for ergodic diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 22(2), pages 233-261, July.
    19. Uchida, Masayuki & Yoshida, Nakahiro, 2013. "Quasi likelihood analysis of volatility and nondegeneracy of statistical random field," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2851-2876.
    20. Nakahiro Yoshida, 2011. "Polynomial type large deviation inequalities and quasi-likelihood analysis for stochastic differential equations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(3), pages 431-479, June.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:scjsta:v:51:y:2024:i:3:p:1181-1205. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.