IDEAS home Printed from https://ideas.repec.org/p/wuu/wpaper/hsc0203.html
   My bibliography  Save this paper

Simulation of Pickands constants

Author

Listed:
  • Krzysztof Burnecki
  • Zbigniew Michna

Abstract

Pickands constants appear in the asymptotic formulas for extremes of Gaussian processes. The explicit formula of Pickands constants does not exist. Moreover, in the literature there is no numerical approximation. In this paper we compute numerically Pickands constants by the use of change of measure technique. To this end we apply two different algorithms to simulate fractional Brownian motion. Finally, we compare the approximations with a theoretical hypothesis and a recently obtained lower bound on the constants. The results justify the hypothesis.

Suggested Citation

  • Krzysztof Burnecki & Zbigniew Michna, 2002. "Simulation of Pickands constants," HSC Research Reports HSC/02/03, Hugo Steinhaus Center, Wroclaw University of Technology.
  • Handle: RePEc:wuu:wpaper:hsc0203
    as

    Download full text from publisher

    File URL: http://www.im.pwr.wroc.pl/~hugo/RePEc/wuu/wpaper/HSC_02_03.pdf
    File Function: Final draft, 2002
    Download Restriction: no

    File URL: http://www.math.uni.wroc.pl/~pms/files/22.1/Article/22.1.14.pdf
    File Function: Final printed version, 2002
    Download Restriction: no

    References listed on IDEAS

    as
    1. Tal Garber & Jacob Goldenberg & Barak Libai & Eitan Muller, 2004. "From Density to Destiny: Using Spatial Dimension of Sales Data for Early Prediction of New Product Success," Marketing Science, INFORMS, vol. 23(3), pages 419-428, August.
    2. repec:wsi:ijmpcx:v:13:y:2002:i:01:n:s0129183102003000 is not listed on IDEAS
    3. repec:wsi:ijmpcx:v:11:y:2000:i:06:n:s0129183100000936 is not listed on IDEAS
    4. Kacperski, Krzysztof & Hołyst, Janusz A., 2000. "Phase transitions as a persistent feature of groups with leaders in models of opinion formation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 631-643.
    5. Frank M. Bass, 1969. "A New Product Growth for Model Consumer Durables," Management Science, INFORMS, pages 215-227.
    6. F. Slanina & H. Lavicka, 2003. "Analytical results for the Sznajd model of opinion formation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 35(2), pages 279-288, September.
    7. Sznajd-Weron, K. & Weron, R., 2003. "How effective is advertising in duopoly markets?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 437-444.
    8. Jacob Goldenberg & Oded Lowengart & Daniel Shapira, 2009. "Zooming In: Self-Emergence of Movements in New Product Growth," Marketing Science, INFORMS, vol. 28(2), pages 274-292, 03-04.
    9. Weyant, John P., 2011. "Accelerating the development and diffusion of new energy technologies: Beyond the "valley of death"," Energy Economics, Elsevier, vol. 33(4), pages 674-682, July.
    10. K. Sznajd-Weron & R. Weron, 2002. "A Simple Model Of Price Formation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., pages 115-123.
    11. Katarzyna Sznajd-Weron & Józef Sznajd, 2000. "Opinion Evolution In Closed Community," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., pages 1157-1165.
    12. Galam, Serge & Vignes, Annick, 2005. "Fashion, novelty and optimality: an application from Physics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 351(2), pages 605-619.
    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. Dëbicki, Krzysztof & Kisowski, Pawel, 2008. "A note on upper estimates for Pickands constants," Statistics & Probability Letters, Elsevier, pages 2046-2051.

    More about this item

    Keywords

    Pickands constant; fractional Brownian motion; change of measure; Cholesky factorization; fGp algorithm;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

    Statistics

    Access and download statistics

    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:wuu:wpaper:hsc0203. 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: (Rafal Weron). General contact details of provider: http://edirc.repec.org/data/hspwrpl.html .

    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.

    We have no references for this item. You can help adding them by using 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.