IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v277y2000i1p25-34.html
   My bibliography  Save this article

Statistical analysis of successive random additions for generating fractional Brownian motion

Author

Listed:
  • McGaughey, Donald R
  • Aitken, George J.M

Abstract

Successive random addition (SRA) is a popular and efficient algorithm for generating fractional Brownian motion (FBM). The difference of adjacent samples of FBM is called fractional Gaussian noise (FGN) and has a known self-similarity parameter H and power spectral density (PSD). For a FGN series generated from the differences of a SRA series, the intersample correlations for the first two lags are known to vary from the desired correlation. In this paper we show analytically and experimentally that the error in the correlations arises because the FGN generated from the differences of an SRA time-series is nonstationary.

Suggested Citation

  • McGaughey, Donald R & Aitken, George J.M, 2000. "Statistical analysis of successive random additions for generating fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 277(1), pages 25-34.
    • Handle: RePEc:eee:phsmap:v:277:y:2000:i:1:p:25-34
    DOI: 10.1016/S0378-4371(99)00438-0
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437199004380
    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/S0378-4371(99)00438-0?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. Caccia, David C. & Percival, Donald & Cannon, Michael J. & Raymond, Gary & Bassingthwaighte, James B., 1997. "Analyzing exact fractal time series: evaluating dispersional analysis and rescaled range methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 609-632.
    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. McGaughey, Donald R. & Aitken, G.J.M., 2002. "Generating two-dimensional fractional Brownian motion using the fractional Gaussian process (FGp) algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 311(3), pages 369-380.
    2. Almurad, Zainy M.H. & Delignières, Didier, 2016. "Evenly spacing in Detrended Fluctuation Analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 63-69.
    3. Hartmann, András & Mukli, Péter & Nagy, Zoltán & Kocsis, László & Hermán, Péter & Eke, András, 2013. "Real-time fractal signal processing in the time domain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(1), pages 89-102.
    4. Mante, Claude, 2007. "Application of resampling and linear spline methods to spectral and dispersional analyses of long-memory processes," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4308-4323, May.
    5. Peter F. Craigmile, 2003. "Simulating a class of stationary Gaussian processes using the Davies–Harte algorithm, with application to long memory processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(5), pages 505-511, September.
    6. Philipp Kainz & Michael Mayrhofer-Reinhartshuber & Helmut Ahammer, 2015. "IQM: An Extensible and Portable Open Source Application for Image and Signal Analysis in Java," PLOS ONE, Public Library of Science, vol. 10(1), pages 1-28, January.
    7. M. Soorya Gayathri & S. Adarsh & K. Shehinamol & Zaina Nizamudeen & Mahima R. Lal, 2023. "Evaluation of change points and persistence of extreme climatic indices across India," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 116(2), pages 2747-2759, March.
    8. Hendrik J. Blok, 2000. "On the nature of the stock market: Simulations and experiments," Papers cond-mat/0010211, arXiv.org.
    9. Alvarez-Ramirez, Jose & Echeverria, Juan C. & Rodriguez, Eduardo, 2008. "Performance of a high-dimensional R/S method for Hurst exponent estimation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(26), pages 6452-6462.
    10. Biermé, Hermine & Meerschaert, Mark M. & Scheffler, Hans-Peter, 2007. "Operator scaling stable random fields," Stochastic Processes and their Applications, Elsevier, vol. 117(3), pages 312-332, March.
    11. Fu, Yang & Zheng, Zeyu & Xiao, Rui & Shi, Haibo, 2017. "Comparison of two fractal interpolation methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 563-571.
    12. Turvey, Calum G., 2007. "A note on scaled variance ratio estimation of the Hurst exponent with application to agricultural commodity prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 155-165.

    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:277:y:2000:i:1:p:25-34. 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.