IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v391y2012i22p5465-5472.html
   My bibliography  Save this article

Mackey–Glass equation driven by fractional Brownian motion

Author

Listed:
  • Nguyen, Dung Tien

Abstract

In this paper we introduce a fractional stochastic version of the Mackey–Glass model which is a potential candidate to model objects in biology and finance. By a semi-martingale approximate approach we find an semi-analytical expression for the solution.

Suggested Citation

  • Nguyen, Dung Tien, 2012. "Mackey–Glass equation driven by fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5465-5472.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:22:p:5465-5472
    DOI: 10.1016/j.physa.2012.06.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437112005109
    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.2012.06.013?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. Catherine Kyrtsou & Michel Terraza, 2003. "Is it Possible to Study Chaotic and ARCH Behaviour Jointly? Application of a Noisy Mackey–Glass Equation with Heteroskedastic Errors to the Paris Stock Exchange Returns Series," Computational Economics, Springer;Society for Computational Economics, vol. 21(3), pages 257-276, June.
    2. Catherine Kyrtsou & Michel Terraza, 2010. "Seasonal Mackey–Glass–GARCH process and short-term dynamics," Empirical Economics, Springer, vol. 38(2), pages 325-345, April.
    3. Tabak, Benjamin M. & Cajueiro, Daniel O., 2005. "The long-range dependence behavior of the term structure of interest rates in Japan," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 418-426.
    4. Cajueiro, Daniel O. & Tabak, Benjamin M., 2005. "Testing for long range dependence in banking equity indices," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1423-1428.
    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. Nguyen Tien, Dung, 2013. "A stochastic Ginzburg–Landau equation with impulsive effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 1962-1971.

    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. Yin, Xin-An & Yang, Xiao-Hua & Yang, Zhi-Feng, 2009. "Using the R/S method to determine the periodicity of time series," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 731-745.
    2. Liu, Li, 2014. "Cross-correlations between crude oil and agricultural commodity markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 293-302.
    3. Rachida Hennani & Michel Terraza, 2015. "Contributions of a noisy chaotic model to the stressed Value-at-Risk," Economics Bulletin, AccessEcon, vol. 35(2), pages 1262-1273.
    4. Cajueiro, Daniel O. & Tabak, Benjamin M., 2007. "Time-varying long-range dependence in US interest rates," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 360-367.
    5. Kyrtsou, Catherine & Malliaris, Anastasios G. & Serletis, Apostolos, 2009. "Energy sector pricing: On the role of neglected nonlinearity," Energy Economics, Elsevier, vol. 31(3), pages 492-502, May.
    6. Rachida Hennani, 2015. "Can the Lasota(1977)’s model compete with the Mackey-Glass(1977)’s model in nonlinear modelling of financial time series?," Working Papers 15-09, LAMETA, Universtiy of Montpellier, revised Jun 2015.
    7. Mohamed CHIKHI & Claude DIEBOLT, 2022. "Testing the weak form efficiency of the French ETF market with the LSTAR-ANLSTGARCH approach using a semiparametric estimation," Eastern Journal of European Studies, Centre for European Studies, Alexandru Ioan Cuza University, vol. 13, pages 228-253, June.
    8. Foad Shokrollahi & Marcin Marcin Magdziarz, 2020. "Equity warrant pricing under subdiffusive fractional Brownian motion of the short rate," Papers 2007.12228, arXiv.org, revised Nov 2020.
    9. Takami, Marcelo Yoshio & Tabak, Benjamin Miranda, 2008. "Interest rate option pricing and volatility forecasting: An application to Brazil," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 755-763.
    10. Constantinos VORLOW & Antonios ANTONIOU & Catherine KYRTSOU, 2004. "Surrogate Data Analysis and Stochastic Chaotic Modelling: Application to Stock Exchange Returns Series," Computing in Economics and Finance 2004 27, Society for Computational Economics.
    11. Wang, Xiao-Tian & Wu, Min & Zhou, Ze-Min & Jing, Wei-Shu, 2012. "Pricing European option with transaction costs under the fractional long memory stochastic volatility model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1469-1480.
    12. Kyrtsou, Catherine & Labys, Walter C., 2006. "Evidence for chaotic dependence between US inflation and commodity prices," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 256-266, March.
    13. Gerlich, Nikolas & Rostek, Stefan, 2015. "Estimating serial correlation and self-similarity in financial time series—A diversification approach with applications to high frequency data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 434(C), pages 84-98.
    14. Zhongxing Wang & Yan Yan & Xiaosong Chen, 2016. "Long-range Correlation and Market Segmentation in Bond Market," Papers 1610.09812, arXiv.org.
    15. Elena Olmedo, 2014. "Forecasting Spanish Unemployment Using Near Neighbour and Neural Net Techniques," Computational Economics, Springer;Society for Computational Economics, vol. 43(2), pages 183-197, February.
    16. Debi P Bal & Badri N Rath, 2019. "Nonlinear causality between crude oil price and exchange rate: A comparative study of China and India - A Reassessment," Economics Bulletin, AccessEcon, vol. 39(1), pages 592-604.
    17. Claude Diebolt & Catherine Kyrtsou, 2006. "Non-Linear Perspectives for Population and Output Dynamics: New Evidence for Cliometrics," Working Papers 06-02, Association Française de Cliométrie (AFC).
    18. Lautier, Delphine & Raynaud, Franck, 2011. "Statistical properties of derivatives: A journey in term structures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 2009-2019.
    19. Constantinos E. Vorlow, 2004. "Stock Price Clustering and Discreteness: The "Compass Rose" and Predictability," Papers cond-mat/0408013, arXiv.org.
    20. Dagum, Estela Bee & Giannerini, Simone, 2006. "A critical investigation on detrending procedures for non-linear processes," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 175-191, March.

    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:391:y:2012:i:22:p:5465-5472. 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.