IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v45y1997i3p325-345.html
   My bibliography  Save this article

Range reliability in random walks

Author

Listed:
  • Pierre Vallois
  • Charles Tapiero

Abstract

This paper introduces a definition of reliability based on a process range. Thus, process failure is defined when the range of a process first reaches a given and unacceptable level. The Mean Time To Failure (MTTF) which is denned as the mean of the first time for a range to attain a given amplitude is then calculated for an asymmetric random walk process. The probability distribution of the range is then given and the process reliability over long periods of system operations are then calculated. Applications such as the control of wings movements, stock price and exchange rates volatility (defined in terms of reliability) are also used to motivate the usefulness of range processes in reliability studies. Finally, we point out that there is necessarily a relationship between the range reliability and the propensity of a series to become chaotic. Copyright Physica-Verlag 1997

Suggested Citation

  • Pierre Vallois & Charles Tapiero, 1997. "Range reliability in random walks," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(3), pages 325-345, October.
    • Handle: RePEc:spr:mathme:v:45:y:1997:i:3:p:325-345
    DOI: 10.1007/BF01194783
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/BF01194783
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/BF01194783?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. Nelson, Daniel B & Foster, Dean P, 1994. "Asymptotic Filtering Theory for Univariate ARCH Models," Econometrica, Econometric Society, vol. 62(1), pages 1-41, January.
    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. Tapiero, Charles S. & Vallois, Pierre, 2016. "Fractional randomness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1161-1177.
    2. Etienne Tanré & Pierre Vallois, 2006. "Range of Brownian Motion with Drift," Journal of Theoretical Probability, Springer, vol. 19(1), pages 45-69, January.
    3. Vallois, Pierre & Tapiero, Charles S., 2008. "Volatility estimators and the inverse range process in a random volatility random walk and Wiener processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(11), pages 2565-2574.

    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. Christoffersen, Peter & Heston, Steven & Jacobs, Kris, 2010. "Option Anomalies and the Pricing Kernel," Working Papers 11-17, University of Pennsylvania, Wharton School, Weiss Center.
    2. McMillan, David G. & Speight, Alan E. H., 2001. "Non-ferrous metals price volatility: a component analysis," Resources Policy, Elsevier, vol. 27(3), pages 199-207, September.
    3. Anders Tolver Jensen & Theis Lange, 2009. "On IGARCH and convergence of the QMLE for misspecified GARCH models," CREATES Research Papers 2009-06, Department of Economics and Business Economics, Aarhus University.
    4. Kuper, Gerard H. & Lestano, 2007. "Dynamic conditional correlation analysis of financial market interdependence: An application to Thailand and Indonesia," Journal of Asian Economics, Elsevier, vol. 18(4), pages 670-684, August.
    5. Shirley J. Huang & Qianqiu Liu & Jun Yu, 2007. "Realized Daily Variance of S&P 500 Cash Index: A Revaluation of Stylized Facts," Annals of Economics and Finance, Society for AEF, vol. 8(1), pages 33-56, May.
    6. Thomakos, Dimitrios D. & Wang, Tao, 2003. "Realized volatility in the futures markets," Journal of Empirical Finance, Elsevier, vol. 10(3), pages 321-353, May.
    7. Drost, Feike C. & Werker, Bas J. M., 1996. "Closing the GARCH gap: Continuous time GARCH modeling," Journal of Econometrics, Elsevier, vol. 74(1), pages 31-57, September.
    8. F. Fornari & A. Mele, 1998. "ARCH Models and Option Pricing : The Continuous Time Connection," THEMA Working Papers 98-30, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    9. Amilon, Henrik, 2008. "Estimation of an adaptive stock market model with heterogeneous agents," Journal of Empirical Finance, Elsevier, vol. 15(2), pages 342-362, March.
    10. David McMillan & Alan Speight, 2006. "Heterogeneous information flows and intra-day volatility dynamics: evidence from the UK FTSE-100 stock index futures market," Applied Financial Economics, Taylor & Francis Journals, vol. 16(13), pages 959-972.
    11. Daniel B. Nelson, 1994. "Asymptotically Optimal Smoothing with ARCH Models," NBER Technical Working Papers 0161, National Bureau of Economic Research, Inc.
    12. Deschamps, Philippe J., 2012. "Bayesian estimation of generalized hyperbolic skewed student GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3035-3054.
    13. Paolella, Marc S. & Polak, Paweł, 2015. "ALRIGHT: Asymmetric LaRge-scale (I)GARCH with Hetero-Tails," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 282-297.
    14. Sizova, Natalia, 2011. "Integrated variance forecasting: Model based vs. reduced form," Journal of Econometrics, Elsevier, vol. 162(2), pages 294-311, June.
    15. Tu, Anthony H. & Wang, Ming-Chun, 2007. "The innovations of e-mini contracts and futures price volatility components: The empirical investigation of S&P 500 stock index futures," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 17(2), pages 198-211, April.
    16. T.J. Flavin & M.R. Wickens, 2003. "Macroeconomic influences on optimal asset allocation," Review of Financial Economics, John Wiley & Sons, vol. 12(2), pages 207-231.
    17. Antoniou, Antonios & Koutmos, Gregory & Pericli, Andreas, 2005. "Index futures and positive feedback trading: evidence from major stock exchanges," Journal of Empirical Finance, Elsevier, vol. 12(2), pages 219-238, March.
    18. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    19. Vozlyublennaia, Nadia & Meshcheryakov, Artem, 2014. "Dynamic correlation structure and security risk," Journal of Economics and Business, Elsevier, vol. 73(C), pages 48-64.
    20. Nelson, Daniel B. & Foster, Dean P., 1995. "Filtering and forecasting with misspecified ARCH models II : Making the right forecast with the wrong model," Journal of Econometrics, Elsevier, vol. 67(2), pages 303-335, June.

    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:spr:mathme:v:45:y:1997:i:3:p:325-345. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.