IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v123y2019icp347-355.html
   My bibliography  Save this article

Fractional Brownian motion: Difference iterative forecasting models

Author

Listed:
  • Song, Wanqing
  • Li, Ming
  • Li, Yuanyuan
  • Cattani, Carlo
  • Chi, Chi-Hung

Abstract

Forecasting non-stationary stochastic time series represents a rather complex problem. The reason is that such temporal series are not only self-similar but also exhibit a Long-Range Dependence (LRD). As it is known, the Fractional Brown Motion (FBM) can generate a non-stationary stochastic time series with self-similarity and LRD. In this study we investigate the properties of the LRD for identification of self-similarity and the LRD of non-stationary stochastic series by Hurst exponent. Parameter estimation is proposed for Stochastic differential Equation (SDE) of FBM based on Maximum Likelihood Estimation (MLE), and proves the convergence of MLE. The SDE is discretized.The difference equation constructed is the prediction model of the iterative format based on FBM. Monte Carlo simulation is applied to check the validity and accuracy of parameter estimation. We also give a practical example to demonstrate the appropriateness of the predictive model.

Suggested Citation

  • Song, Wanqing & Li, Ming & Li, Yuanyuan & Cattani, Carlo & Chi, Chi-Hung, 2019. "Fractional Brownian motion: Difference iterative forecasting models," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 347-355.
    • Handle: RePEc:eee:chsofr:v:123:y:2019:i:c:p:347-355
    DOI: 10.1016/j.chaos.2019.04.021
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077919301316
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2019.04.021?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. Barunik, Jozef & Kristoufek, Ladislav, 2010. "On Hurst exponent estimation under heavy-tailed distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3844-3855.
    2. Li, Ming & Li, Jia-Yue, 2017. "Generalized Cauchy model of sea level fluctuations with long-range dependence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 309-335.
    3. Lobato, I. & Robinson, P. M., 1996. "Averaged periodogram estimation of long memory," Journal of Econometrics, Elsevier, vol. 73(1), pages 303-324, July.
    4. Li, Ming, 2017. "Record length requirement of long-range dependent teletraffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 472(C), pages 164-187.
    5. Cipian Necula, 2008. "Option Pricing in a Fractional Brownian Motion Environment," Advances in Economic and Financial Research - DOFIN Working Paper Series 2, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.
    6. Longjin, Lv & Ren, Fu-Yao & Qiu, Wei-Yuan, 2010. "The application of fractional derivatives in stochastic models driven by fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4809-4818.
    7. Céline Lévy‐Leduc & Hélène Boistard & Eric Moulines & Murad S. Taqqu & Valderio A. Reisen, 2011. "Robust estimation of the scale and of the autocovariance function of Gaussian short‐ and long‐range dependent processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(2), pages 135-156, March.
    8. Mielniczuk, J. & Wojdyllo, P., 2007. "Estimation of Hurst exponent revisited," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4510-4525, May.
    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. Zeinali, Narges & Pourdarvish, Ahmad, 2022. "An entropy-based estimator of the Hurst exponent in fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 591(C).
    2. Li, Ming & Wang, Anqi, 2020. "Fractal teletraffic delay bounds in computer networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    3. Liu, He & Song, Wanqing & Li, Ming & Kudreyko, Aleksey & Zio, Enrico, 2020. "Fractional Lévy stable motion: Finite difference iterative forecasting model," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    4. Li, Ming, 2021. "Generalized fractional Gaussian noise and its application to traffic modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 579(C).
    5. Song, Wanqing & Cattani, Carlo & Chi, Chi-Hung, 2020. "Multifractional Brownian motion and quantum-behaved particle swarm optimization for short term power load forecasting: An integrated approach," Energy, Elsevier, vol. 194(C).

    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. Song, Wanqing & Cattani, Carlo & Chi, Chi-Hung, 2020. "Multifractional Brownian motion and quantum-behaved particle swarm optimization for short term power load forecasting: An integrated approach," Energy, Elsevier, vol. 194(C).
    2. Li, Ming & Zhang, Peidong & Leng, Jianxing, 2016. "Improving autocorrelation regression for the Hurst parameter estimation of long-range dependent time series based on golden section search," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 189-199.
    3. Li, Ming & Li, Jia-Yue, 2017. "Generalized Cauchy model of sea level fluctuations with long-range dependence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 309-335.
    4. Auer, Benjamin R., 2016. "On the performance of simple trading rules derived from the fractal dynamics of gold and silver price fluctuations," Finance Research Letters, Elsevier, vol. 16(C), pages 255-267.
    5. Mulligan, Robert F., 2017. "The multifractal character of capacity utilization over the business cycle: An application of Hurst signature analysis," The Quarterly Review of Economics and Finance, Elsevier, vol. 63(C), pages 147-152.
    6. Avci-Surucu, Ezgi & Aydogan, A. Kursat & Akgul, Doganbey, 2016. "Bidding structure, market efficiency and persistence in a multi-time tariff setting," Energy Economics, Elsevier, vol. 54(C), pages 77-87.
    7. Benjamin Rainer Auer, 2018. "Are standard asset pricing factors long-range dependent?," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 42(1), pages 66-88, January.
    8. Li, Ming & Wang, Anqi, 2020. "Fractal teletraffic delay bounds in computer networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    9. Auer, Benjamin R., 2016. "On time-varying predictability of emerging stock market returns," Emerging Markets Review, Elsevier, vol. 27(C), pages 1-13.
    10. Reisen, Valdério Anselmo & Monte, Edson Zambon & da Conceição Franco, Glaura & Sgrancio, Adriano Marcio & Molinares, Fábio Alexander Fajardo & Bondon, Pascal & Ziegelmann, Flávio Augusto & Abraham, Bo, 2018. "Robust estimation of fractional seasonal processes: Modeling and forecasting daily average SO2 concentrations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 146(C), pages 27-43.
    11. Li, Daye & Nishimura, Yusaku & Men, Ming, 2016. "The long memory and the transaction cost in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 312-320.
    12. Li, Ming, 2020. "Multi-fractional generalized Cauchy process and its application to teletraffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 550(C).
    13. Liu, He & Song, Wanqing & Li, Ming & Kudreyko, Aleksey & Zio, Enrico, 2020. "Fractional Lévy stable motion: Finite difference iterative forecasting model," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    14. Li, Ming, 2021. "Generalized fractional Gaussian noise and its application to traffic modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 579(C).
    15. Lotfalinezhad, Hamze & Maleki, Ali, 2020. "TTA, a new approach to estimate Hurst exponent with less estimation error and computational time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    16. Mulligan, Robert F., 2014. "Multifractality of sectoral price indices: Hurst signature analysis of Cantillon effects in disequilibrium factor markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 252-264.
    17. Benjamin R Auer, 2016. "Pure return persistence, Hurst exponents and hedge fund selection – A practical note," Journal of Asset Management, Palgrave Macmillan, vol. 17(5), pages 319-330, September.
    18. Jean-Philippe Aguilar & Jan Korbel & Yuri Luchko, 2019. "Applications of the Fractional Diffusion Equation to Option Pricing and Risk Calculations," Mathematics, MDPI, vol. 7(9), pages 1-23, September.
    19. Pakrashi, Vikram & Kelly, Joe & Harkin, Julie & Farrell, Aidan, 2013. "Hurst exponent footprints from activities on a large structural system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(8), pages 1803-1817.
    20. Jiang, Yonghong & Nie, He & Ruan, Weihua, 2018. "Time-varying long-term memory in Bitcoin market," Finance Research Letters, Elsevier, vol. 25(C), pages 280-284.

    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:chsofr:v:123:y:2019:i:c:p:347-355. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.