IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v450y2016icp294-304.html
   My bibliography  Save this article

A robust nonparametric framework for reconstruction of stochastic differential equation models

Author

Listed:
  • Rajabzadeh, Yalda
  • Rezaie, Amir Hossein
  • Amindavar, Hamidreza

Abstract

In this paper, we employ a nonparametric framework to robustly estimate the functional forms of drift and diffusion terms from discrete stationary time series. The proposed method significantly improves the accuracy of the parameter estimation. In this framework, drift and diffusion coefficients are modeled through orthogonal Legendre polynomials. We employ the least squares regression approach along with the Euler–Maruyama approximation method to learn coefficients of stochastic model. Next, a numerical discrete construction of mean squared prediction error (MSPE) is established to calculate the order of Legendre polynomials in drift and diffusion terms. We show numerically that the new method is robust against the variation in sample size and sampling rate. The performance of our method in comparison with the kernel-based regression (KBR) method is demonstrated through simulation and real data. In case of real dataset, we test our method for discriminating healthy electroencephalogram (EEG) signals from epilepsy ones. We also demonstrate the efficiency of the method through prediction in the financial data. In both simulation and real data, our algorithm outperforms the KBR method.

Suggested Citation

  • Rajabzadeh, Yalda & Rezaie, Amir Hossein & Amindavar, Hamidreza, 2016. "A robust nonparametric framework for reconstruction of stochastic differential equation models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 294-304.
    • Handle: RePEc:eee:phsmap:v:450:y:2016:i:c:p:294-304
    DOI: 10.1016/j.physa.2016.01.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437116000248
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2016.01.016?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. Lim, Gyuchang & Kim, SooYong & Scalas, Enrico & Kim, Kyungsik & Chang, Ki-Ho, 2008. "Analysis of price fluctuations in futures exchange markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(12), pages 2823-2830.
    2. C. Renner & J. Peinke & R. Friedrich, 2001. "Markov properties of high frequency exchange rate data," Papers cond-mat/0102494, arXiv.org, revised Apr 2001.
    3. Renner, Ch. & Peinke, J. & Friedrich, R., 2001. "Evidence of Markov properties of high frequency exchange rate data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 298(3), pages 499-520.
    4. P. Rinn & H. Heißelmann & M. Wächter & J. Peinke, 2013. "Stochastic method for in-situ damage analysis," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 86(1), pages 1-5, January.
    5. Farahpour, F. & Eskandari, Z. & Bahraminasab, A. & Jafari, G.R. & Ghasemi, F. & Sahimi, Muhammad & Reza Rahimi Tabar, M., 2007. "A Langevin equation for the rates of currency exchange based on the Markov analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 601-608.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Théo Michelot & Richard Glennie & Catriona Harris & Len Thomas, 2021. "Varying-Coefficient Stochastic Differential Equations with Applications in Ecology," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(3), pages 446-463, September.

    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. Wosnitza, Jan Henrik & Leker, Jens, 2014. "Can log-periodic power law structures arise from random fluctuations?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 228-250.
    2. Kozaki, M. & Sato, A.-H., 2008. "Application of the Beck model to stock markets: Value-at-Risk and portfolio risk assessment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1225-1246.
    3. Jun-ichi Maskawa & Koji Kuroda, 2020. "Model of continuous random cascade processes in financial markets," Papers 2010.12270, arXiv.org.
    4. G. L. Buchbinder & K. M. Chistilin, 2006. "Multiple time scales and the empirical models for stochastic volatility," Papers physics/0611048, arXiv.org.
    5. Ausloos, Marcel & Ivanova, Kristinka & Siwy, Zuzanna, 2004. "Searching for self-similarity in switching time and turbulent cascades in ion transport through a biochannel. A time delay asymmetry," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(3), pages 319-333.
    6. Wolfgang Hardle & Torsten Kleinow & Alexander Korostelev & Camille Logeay & Eckhard Platen, 2008. "Semiparametric diffusion estimation and application to a stock market index," Quantitative Finance, Taylor & Francis Journals, vol. 8(1), pages 81-92.
    7. Seemann, Lars & Hua, Jia-Chen & McCauley, Joseph L. & Gunaratne, Gemunu H., 2012. "Ensemble vs. time averages in financial time series analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 6024-6032.
    8. Oya, Shunsuke & Aihara, Kazuyuki & Hirata, Yoshito, 2014. "An absolute measure for a key currency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 15-23.
    9. Hirata, Yoshito & Aihara, Kazuyuki, 2012. "Timing matters in foreign exchange markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 760-766.
    10. Buchbinder, G.L. & Chistilin, K.M., 2007. "Multiple time scales and the empirical models for stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(1), pages 168-178.
    11. Wenxin Yu & Shoudao Huang & Weihong Xiao, 2018. "Fault Diagnosis Based on an Approach Combining a Spectrogram and a Convolutional Neural Network with Application to a Wind Turbine System," Energies, MDPI, vol. 11(10), pages 1-11, September.
    12. Pedro G. Lind & Luis Vera-Tudela & Matthias Wächter & Martin Kühn & Joachim Peinke, 2017. "Normal Behaviour Models for Wind Turbine Vibrations: Comparison of Neural Networks and a Stochastic Approach," Energies, MDPI, vol. 10(12), pages 1-14, November.
    13. Subbotin, Alexandre, 2009. "Volatility Models: from Conditional Heteroscedasticity to Cascades at Multiple Horizons," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 15(3), pages 94-138.

    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:phsmap:v:450:y:2016:i:c:p:294-304. 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: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.