IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v480y2024ics0096300324003679.html
   My bibliography  Save this article

Deep learning-based estimation of time-dependent parameters in Markov models with application to nonlinear regression and SDEs

Author

Listed:
  • Kałuża, Andrzej
  • Morkisz, Paweł M.
  • Mulewicz, Bartłomiej
  • Przybyłowicz, Paweł
  • Wia̧cek, Martyna

Abstract

We present a novel deep-learning method for estimating time-dependent parameters in Markov processes through discrete sampling. Departing from conventional machine learning, our approach reframes parameter approximation as an optimization problem using the maximum likelihood approach. Experimental validation focuses on parameter estimation in multivariate regression and stochastic differential equations (SDEs). Theoretical results show that the real solution is close to SDE with parameters approximated using our neural network derived under specific conditions. Our work contributes to SDE-based model parameter estimation, offering a versatile tool for diverse fields.

Suggested Citation

  • Kałuża, Andrzej & Morkisz, Paweł M. & Mulewicz, Bartłomiej & Przybyłowicz, Paweł & Wia̧cek, Martyna, 2024. "Deep learning-based estimation of time-dependent parameters in Markov models with application to nonlinear regression and SDEs," Applied Mathematics and Computation, Elsevier, vol. 480(C).
    • Handle: RePEc:eee:apmaco:v:480:y:2024:i:c:s0096300324003679
    DOI: 10.1016/j.amc.2024.128906
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300324003679
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2024.128906?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Maud Delattre & Valentine Genon-Catalot & Adeline Samson, 2013. "Maximum Likelihood Estimation for Stochastic Differential Equations with Random Effects," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(2), pages 322-343, June.
    3. Long, Hongwei & Ma, Chunhua & Shimizu, Yasutaka, 2017. "Least squares estimators for stochastic differential equations driven by small Lévy noises," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1475-1495.
    4. Nadim Alfouhaili & Frédéric Gautier & Iyad Zaarour, 2020. "The Impact of Basel III Capital Regulation on Credit Risk: A Hybrid Model," International Journal of Finance & Banking Studies, Center for the Strategic Studies in Business and Finance, vol. 9(2), pages 56-71, April.
    5. Andersen, Torben G. & Chung, Hyung-Jin & Sorensen, Bent E., 1999. "Efficient method of moments estimation of a stochastic volatility model: A Monte Carlo study," Journal of Econometrics, Elsevier, vol. 91(1), pages 61-87, July.
    6. Yoshida, Nakahiro, 1992. "Estimation for diffusion processes from discrete observation," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 220-242, May.
    7. Dai, Min & Duan, Jinqiao & Liao, Junjun & Wang, Xiangjun, 2021. "Maximum likelihood estimation of stochastic differential equations with random effects driven by fractional Brownian motion," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    8. Tianhai Tian & Yanli Zhou & Yonghong Wu & Xiangyu Ge, 2014. "Estimation of Parameters in Mean-Reverting Stochastic Systems," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-8, March.
    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. Lô, Serigne N. & Ronchetti, Elvezio, 2012. "Robust small sample accurate inference in moment condition models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3182-3197.
    2. Jianqing Fan, 2004. "A selective overview of nonparametric methods in financial econometrics," Papers math/0411034, arXiv.org.
    3. Meddahi, N., 2001. "An Eigenfunction Approach for Volatility Modeling," Cahiers de recherche 2001-29, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    4. Hlouskova, Jaroslava & Sögner, Leopold, 2020. "GMM estimation of affine term structure models," Econometrics and Statistics, Elsevier, vol. 13(C), pages 2-15.
    5. repec:wyi:journl:002108 is not listed on IDEAS
    6. Bontemps, Christian & Meddahi, Nour, 2005. "Testing normality: a GMM approach," Journal of Econometrics, Elsevier, vol. 124(1), pages 149-186, January.
    7. A. S. Hurn & J. I. Jeisman & K. A. Lindsay, 0. "Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations," Journal of Financial Econometrics, Oxford University Press, vol. 5(3), pages 390-455.
    8. Grammig, Joachim & Schaub, Eva-Maria, 2014. "Give me strong moments and time - Combining GMM and SMM to estimate long-run risk asset pricing models," VfS Annual Conference 2014 (Hamburg): Evidence-based Economic Policy 100607, Verein für Socialpolitik / German Economic Association.
    9. Grammig, Joachim & Schaub, Eva-Maria, 2014. "Give me strong moments and time: Combining GMM and SMM to estimate long-run risk asset pricing," CFR Working Papers 14-05, University of Cologne, Centre for Financial Research (CFR).
    10. repec:bla:ecorec:v:91:y:2015:i::p:1-24 is not listed on IDEAS
    11. Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91(S1), pages 1-24, June.
    12. Pascale VALERY (HEC-Montreal) & Jean-Marie Dufour (University of Montreal), 2004. "A simple estimation method and finite-sample inference for a stochastic volatility model," Econometric Society 2004 North American Summer Meetings 153, Econometric Society.
    13. Michael Sørensen, 2008. "Parametric inference for discretely sampled stochastic differential equations," CREATES Research Papers 2008-18, Department of Economics and Business Economics, Aarhus University.
    14. Grammig, Joachim & Schaub, Eva-Maria, 2014. "Give me strong moments and time: Combining GMM and SMM to estimate long-run risk asset pricing models," CFS Working Paper Series 479, Center for Financial Studies (CFS).
    15. Yiying Cheng & Yaozhong Hu & Hongwei Long, 2020. "Generalized moment estimators for $$\alpha $$α-stable Ornstein–Uhlenbeck motions from discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 53-81, April.
    16. 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.
    17. Zhang, Shulin & Song, Peter X.-K. & Shi, Daimin & Zhou, Qian M., 2012. "Information ratio test for model misspecification on parametric structures in stochastic diffusion models," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3975-3987.
    18. Yoonsuk Lee & B. Wade Brorsen, 2017. "Permanent Breaks and Temporary Shocks in a Time Series," Computational Economics, Springer;Society for Computational Economics, vol. 49(2), pages 255-270, February.
    19. Carmen Broto & Esther Ruiz, 2004. "Estimation methods for stochastic volatility models: a survey," Journal of Economic Surveys, Wiley Blackwell, vol. 18(5), pages 613-649, December.
    20. J. Jimenez & R. Biscay & T. Ozaki, 2005. "Inference Methods for Discretely Observed Continuous-Time Stochastic Volatility Models: A Commented Overview," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 12(2), pages 109-141, June.
    21. Zongwu Cai & Yongmiao Hong, 2013. "Some Recent Developments in Nonparametric Finance," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    22. Gallant, A. Ronald & Tauchen, George, 2002. "Simulated Score Methods and Indirect Inference for Continuous-time Models," Working Papers 02-09, Duke University, Department of Economics.

    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:eee:apmaco:v:480:y:2024:i:c:s0096300324003679. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.