IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v241y1997i3p606-626.html
   My bibliography  Save this article

Evaluating scaled windowed variance methods for estimating the Hurst coefficient of time series

Author

Listed:
  • Cannon, Michael J.
  • Percival, Donald B.
  • Caccia, David C.
  • Raymond, Gary M.
  • Bassingthwaighte, James B.

Abstract

Three-scaled windowed variance methods (standard, linear regression detrended, and bridge detrended) for estimating the Hurst coefficient (H) are evaluated. The Hurst coefficient, with 0 < H < 1, characterizes self-similar decay in the time-series autocorrelation function. The scaled windowed variance methods estimate H for fractional Brownian motion (fBm) signals which are cumulative sums of fractional Gaussian noise (fGn) signals. For all three methods both the bias and standard deviation of estimates are less than 0.05 for series having N ⩾ 29 points. Estimates for short series (N < 28) are unreliable. To have a 0.95 probability of distinguishing between two signals with true H differing by 0.1, more than 215 points are needed. All three methods proved more reliable (based on bias and variance of estimates) than Hurst's rescaled range analysis, periodogram analysis, and autocorrelation analysis, and as reliable as dispersional analysis. The latter methods can only be applied to fGn or differences of fBm, while the scaled windowed variance methods must be applied to fBm or cumulative sums of fGn.

Suggested Citation

  • Cannon, Michael J. & Percival, Donald B. & Caccia, David C. & Raymond, Gary M. & Bassingthwaighte, James B., 1997. "Evaluating scaled windowed variance methods for estimating the Hurst coefficient of time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 241(3), pages 606-626.
  • Handle: RePEc:eee:phsmap:v:241:y:1997:i:3:p:606-626
    DOI: 10.1016/S0378-4371(97)00252-5
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437197002525
    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

    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. Stanley, H.E. & Buldyrev, S.V. & Goldberger, A.L. & Goldberger, Z.D. & Havlin, S. & Mantegna, R.N. & Ossadnik, S.M. & Peng, C.-K. & Simons, M., 1994. "Statistical mechanics in biology: how ubiquitous are long-range correlations?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 205(1), pages 214-253.
    2. Chandra, Ramesh & Rohrbach, Kermit & Willinger, G Lee, 1995. "A Comparison of the Power of Parametric and Nonparametric Tests of Location Shift for Event Studies," The Financial Review, Eastern Finance Association, vol. 30(4), pages 685-710, November.
    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. Erzgräber, Hartmut & Strozzi, Fernanda & Zaldívar, José-Manuel & Touchette, Hugo & Gutiérrez, Eugénio & Arrowsmith, David K., 2008. "Time series analysis and long range correlations of Nordic spot electricity market data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(26), pages 6567-6574.
    2. Emmanuel Numapau Gyamfi & Adam Anokye Mohammed, 2017. "Validity of Purchasing Power Parity in BRICS under a DFA Approach," Acta Universitatis Danubius. OEconomica, Danubius University of Galati, issue 13(1), pages 17-28, February.
    3. Tan, Pei P. & Galagedera, Don U.A. & Maharaj, Elizabeth A., 2012. "A wavelet based investigation of long memory in stock returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(7), pages 2330-2341.
    4. 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.
    5. Mason, David M., 2016. "The Hurst phenomenon and the rescaled range statistic," Stochastic Processes and their Applications, Elsevier, vol. 126(12), pages 3790-3807.
    6. Alvarez-Ramirez, J. & Echeverria, J.C. & Meraz, M. & Rodriguez, E., 2017. "Asymmetric acceleration/deceleration dynamics in heart rate variability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 213-224.
    7. Kirchner, M. & Schubert, P. & Schmidtbleicher, D. & Haas, C.T., 2012. "Evaluation of the temporal structure of postural sway fluctuations based on a comprehensive set of analysis tools," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4692-4703.
    8. Mukli, Peter & Nagy, Zoltan & Eke, Andras, 2015. "Multifractal formalism by enforcing the universal behavior of scaling functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 150-167.
    9. Ildefonso M De la Fuente & Fernando Vadillo & Alberto Luís Pérez-Samartín & Martín-Blas Pérez-Pinilla & Joseba Bidaurrazaga & Antonio Vera-López, 2010. "Global Self-Regulation of the Cellular Metabolic Structure," PLOS ONE, Public Library of Science, vol. 5(3), pages 1-15, March.
    10. 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.
    11. Emilian Lucian NEACSU & Marcela Daniela TODONI, 2014. "A Way To Determine Chaotic Behaviour In Romanian Stock Market," Review of Economic and Business Studies, Alexandru Ioan Cuza University, Faculty of Economics and Business Administration, issue 14, pages 207-214, December.
    12. Michalski, Sebastian, 2008. "Blocks adjustment—reduction of bias and variance of detrended fluctuation analysis using Monte Carlo simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 217-242.
    13. 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.
    14. 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.
    15. Serinaldi, Francesco, 2010. "Use and misuse of some Hurst parameter estimators applied to stationary and non-stationary financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2770-2781.
    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. Wei, Kun & Zhang, Youxin & Luo, Yi, 2018. "Variance-mediated multifractal analysis of group participation in chasing a single dangerous prey," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 1275-1287.
    18. John Halley & Dimitris Kugiumtzis, 2011. "Nonparametric testing of variability and trend in some climatic records," Climatic Change, Springer, vol. 109(3), pages 549-568, December.

    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:241:y:1997:i:3:p:606-626. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Haili He). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.