IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

Extreme value statistics and recurrence intervals of NYMEX energy futures volatility

  • Wen-Jie Xie


  • Zhi-Qiang Jiang


  • Wei-Xing Zhou


Registered author(s):

    Energy markets and the associated energy futures markets play a crucial role in global economies. We investigate the statistical properties of the recurrence intervals of daily volatility time series of four NYMEX energy futures, which are defined as the waiting times $\tau$ between consecutive volatilities exceeding a given threshold $q$. We find that the recurrence intervals are distributed as a stretched exponential $P_q(\tau)\sim e^{(a\tau)^{-\gamma}}$, where the exponent $\gamma$ decreases with increasing $q$, and there is no scaling behavior in the distributions for different thresholds $q$ after the recurrence intervals are scaled with the mean recurrence interval $\bar\tau$. These findings are significant under the Kolmogorov-Smirnov test and the Cram{\'e}r-von Mises test. We show that empirical estimations are in nice agreement with the numerical integration results for the occurrence probability $W_q(\Delta{t}|t)$ of a next event above the threshold $q$ within a (short) time interval after an elapsed time $t$ from the last event above $q$. We also investigate the memory effects of the recurrence intervals. It is found that the conditional distributions of large and small recurrence intervals differ from each other and the conditional mean of the recurrence intervals scales as a power law of the preceding interval $\bar\tau(\tau_0)/\bar\tau \sim (\tau_0/\bar\tau)^\beta$, indicating that the recurrence intervals have short-term correlations. Detrended fluctuation analysis and detrending moving average analysis further uncover that the recurrence intervals possess long-term correlations. We confirm that the "clustering" of the volatility recurrence intervals is caused by the long-term correlations well known to be present in the volatility.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL:
    File Function: Latest version
    Download Restriction: no

    Paper provided by in its series Papers with number 1211.5502.

    in new window

    Date of creation: Nov 2012
    Date of revision:
    Publication status: Published in Economic Modelling 36, 8-17 (2014)
    Handle: RePEc:arx:papers:1211.5502
    Contact details of provider: Web page:

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

    as in new window
    1. Fei Ren & Gao-Feng Gu & Wei-Xing Zhou, 2009. "Scaling and memory in the return intervals of realized volatility," Papers 0904.1107,, revised Aug 2009.
    2. Ren, Fei & Guo, Liang & Zhou, Wei-Xing, 2009. "Statistical properties of volatility return intervals of Chinese stocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(6), pages 881-890.
    3. Fei Ren & Wei-Xing Zhou, 2008. "Multiscaling behavior in the volatility return intervals of Chinese indices," Papers 0809.0250,
    4. Taisei Kaizoji & Michiyo Kaizoji, 2003. "Power law for the calm-time interval of price changes," Papers cond-mat/0312560,, revised Mar 2006.
    5. F. Wang & P. Weber & K. Yamasaki & S. Havlin & H. E. Stanley, 2007. "Statistical regularities in the return intervals of volatility," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 55(2), pages 123-133, 01.
    6. Matsushita, Raul & Gleria, Iram & Figueiredo, Annibal & Da Silva, Sergio, 2007. "Are Pound and Euro the Same Currency? - Updated," MPRA Paper 1981, University Library of Munich, Germany.
    7. W.-S. Jung & F. Z. Wang & S. Havlin & T. Kaizoji & H.-T. Moon & H. E. Stanley, 2008. "Volatility return intervals analysis of the Japanese market," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 62(1), pages 113-119, 03.
    8. Tabak, Benjamin M. & Cajueiro, Daniel O., 2007. "Are the crude oil markets becoming weakly efficient over time? A test for time-varying long-range dependence in prices and volatility," Energy Economics, Elsevier, vol. 29(1), pages 28-36, January.
    9. Fei Ren & Wei-Xing Zhou, 2010. "Recurrence interval analysis of trading volumes," Papers 1002.1653,
    10. Carbone, Anna & Stanley, H.Eugene, 2004. "Directed self-organized critical patterns emerging from fractional Brownian paths," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(4), pages 544-551.
    11. M. S. Santhanam & Holger Kantz, 2008. "Return interval distribution of extreme events and long term memory," Papers 0803.1706,
    12. Jones, Charles M & Kaul, Gautam, 1996. " Oil and the Stock Markets," Journal of Finance, American Finance Association, vol. 51(2), pages 463-91, June.
    13. Greco, Antonella & Sorriso-Valvo, Luca & Carbone, Vincenzo & Cidone, Stefano, 2008. "Waiting time distributions of the volatility in the Italian MIB30 index: Clustering or Poisson functions?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(16), pages 4272-4284.
    14. Sadorsky, Perry, 1999. "Oil price shocks and stock market activity," Energy Economics, Elsevier, vol. 21(5), pages 449-469, October.
    15. Arianos, Sergio & Carbone, Anna, 2007. "Detrending moving average algorithm: A closed-form approximation of the scaling law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 9-15.
    16. Serletis, Apostolos & Rosenberg, Aryeh Adam, 2007. "The Hurst exponent in energy futures prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 325-332.
    17. Junhuan Zhang & Jun Wang & Jiguang Shao, 2010. "Finite-Range Contact Process On The Market Return Intervals Distributions," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 13(05), pages 643-657.
    18. Ren, Fei & Gu, Gao-Feng & Zhou, Wei-Xing, 2009. "Scaling and memory in the return intervals of realized volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(22), pages 4787-4796.
    19. Elder, John & Serletis, Apostolos, 2008. "Long memory in energy futures prices," Review of Financial Economics, Elsevier, vol. 17(2), pages 146-155.
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:arx:papers:1211.5502. 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: (arXiv administrators)

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 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.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.