IDEAS home Printed from https://ideas.repec.org/p/ags/aaea06/21239.html
   My bibliography  Save this paper

The Confidence Limits of a Geometric Brownian Motion

Author

Listed:
  • Turvey, Calum G.
  • Power, Gabriel J.

Abstract

This paper investigates whether the assumption of Brownian motion often used to describe commodity price movements is satisfied. Using historical data from 17 commodity futures contracts specific tests of fractional and ordinary Brownian motion are conducted. The analyses are conducted under the null hypothesis of ordinary Brownian motion against the alternative of persistent or ergodic fractional Brownian motion. Tests for fractional Brownian motion are based on a variance ratio test. However, standard errors based on Monte Carlo simulations are quite high, meaning that the acceptance region for the null hypothesis is large. The results indicate that for the most part, the null hypothesis of ordinary Brownian motion cannot be rejected for 14 of 17 series. The three series that did not satisfy the tests were rejected because they violated the stationarity property of the random walk hypothesis.

Suggested Citation

  • Turvey, Calum G. & Power, Gabriel J., 2006. "The Confidence Limits of a Geometric Brownian Motion," 2006 Annual meeting, July 23-26, Long Beach, CA 21239, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    • Handle: RePEc:ags:aaea06:21239
    DOI: 10.22004/ag.econ.21239
    as

    Download full text from publisher

    File URL: https://ageconsearch.umn.edu/record/21239/files/sp06tu01.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.22004/ag.econ.21239?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
    ---><---

    References listed on IDEAS

    as
    1. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
    2. Marco Corazza & A.G. Malliaris & Carla Nardelli, 1997. "Searching for fractal structure in agricultural futures markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 17(4), pages 433-473, June.
    3. Billy P. Helms & Fred R. Kaen & Robert E. Rosenman, 1984. "Memory in commodity futures contracts," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 4(4), pages 559-567, December.
    4. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    5. John Barkoulas & Walter C. Labys & Joseph Onochie, 1997. "Fractional dynamics in international commodity prices," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 17(2), pages 161-189, April.
    6. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    7. Hyun J. Jin & Darren L. Frechette, 2004. "Fractional Integration in Agricultural Futures Price Volatilities," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 86(2), pages 432-443.
    8. Benoit B. Mandelbrot, 1972. "Statistical Methodology for Nonperiodic Cycles: From the Covariance To R/S Analysis," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 1, number 3, pages 259-290, National Bureau of Economic Research, Inc.
    9. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    10. Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 246-273, April.
    11. Booth, G. Geoffrey & Kaen, Fred R. & Koveos, Peter E., 1982. "R/S analysis of foreign exchange rates under two international monetary regimes," Journal of Monetary Economics, Elsevier, vol. 10(3), pages 407-415.
    12. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    13. Epaminondas Panas, 2001. "Estimating fractal dimension using stable distributions and exploring long memory through ARFIMA models in Athens Stock Exchange," Applied Financial Economics, Taylor & Francis Journals, vol. 11(4), pages 395-402.
    14. Barkoulas, John T. & Baum, Christopher F., 1996. "Long-term dependence in stock returns," Economics Letters, Elsevier, vol. 53(3), pages 253-259, December.
    15. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-384, March.
    16. Comte, F. & Renault, E., 1996. "Long memory continuous time models," Journal of Econometrics, Elsevier, vol. 73(1), pages 101-149, July.
    17. L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105, January.
    18. P. S. Sephton, 2002. "Fractional cointegration: Monte Carlo estimates of critical values, with an application," Applied Financial Economics, Taylor & Francis Journals, vol. 12(5), pages 331-335.
    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. 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.
    2. Turvey, Calum G., 2001. "Random Walks And Fractal Structures In Agricultural Commodity Futures Prices," Working Papers 34151, University of Guelph, Department of Food, Agricultural and Resource Economics.
    3. Guglielmo Maria Caporale & Luis A. Gil-Alana & Alex Plastun, 2017. "Long Memory and Data Frequency in Financial Markets," CESifo Working Paper Series 6396, CESifo.
    4. Yalama, Abdullah & Celik, Sibel, 2013. "Real or spurious long memory characteristics of volatility: Empirical evidence from an emerging market," Economic Modelling, Elsevier, vol. 30(C), pages 67-72.
    5. Goddard, John & Onali, Enrico, 2012. "Self-affinity in financial asset returns," International Review of Financial Analysis, Elsevier, vol. 24(C), pages 1-11.
    6. Mulligan, Robert F., 2004. "Fractal analysis of highly volatile markets: an application to technology equities," The Quarterly Review of Economics and Finance, Elsevier, vol. 44(1), pages 155-179, February.
    7. Asif, Raheel & Frömmel, Michael, 2022. "Testing Long memory in exchange rates and its implications for the adaptive market hypothesis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 593(C).
    8. Mynhardt, H. R. & Plastun, Alex & Makarenko, Inna, 2014. "Behavior of Financial Markets Efficiency During the Financial Market Crisis: 2007-2009," MPRA Paper 58942, University Library of Munich, Germany.
    9. Robert Mulligan, 2000. "A fractal analysis of foreign exchange markets," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 6(1), pages 33-49, February.
    10. Mulligan, Robert F. & Lombardo, Gary A., 2004. "Maritime businesses: volatile stock prices and market valuation inefficiencies," The Quarterly Review of Economics and Finance, Elsevier, vol. 44(2), pages 321-336, May.
    11. Howe, John S. & Martin, Deryl W. & WoodJr., Bob G., 1999. "Much ado about nothing: Long-term memory in Pacific Rim equity markets," International Review of Financial Analysis, Elsevier, vol. 8(2), pages 139-151, June.
    12. Paul Eitelman & Justin Vitanza, 2008. "A non-random walk revisited: short- and long-term memory in asset prices," International Finance Discussion Papers 956, Board of Governors of the Federal Reserve System (U.S.).
    13. Christian de Peretti, 2003. "Bilateral Bootstrap Tests for Long Memory: An Application to the Silver Market," Computational Economics, Springer;Society for Computational Economics, vol. 22(2), pages 187-212, October.
    14. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    15. Gerlich, Nikolas & Rostek, Stefan, 2015. "Estimating serial correlation and self-similarity in financial time series—A diversification approach with applications to high frequency data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 434(C), pages 84-98.
    16. Vasile Brătian & Ana-Maria Acu & Camelia Oprean-Stan & Emil Dinga & Gabriela-Mariana Ionescu, 2021. "Efficient or Fractal Market Hypothesis? A Stock Indexes Modelling Using Geometric Brownian Motion and Geometric Fractional Brownian Motion," Mathematics, MDPI, vol. 9(22), pages 1-20, November.
    17. Fernández-Martínez, M. & Sánchez-Granero, M.A. & Trinidad Segovia, J.E., 2013. "Measuring the self-similarity exponent in Lévy stable processes of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5330-5345.
    18. Hull, Matthew & McGroarty, Frank, 2014. "Do emerging markets become more efficient as they develop? Long memory persistence in equity indices," Emerging Markets Review, Elsevier, vol. 18(C), pages 45-61.
    19. Power, Gabriel J. & Turvey, Calum G., 2010. "Long-range dependence in the volatility of commodity futures prices: Wavelet-based evidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(1), pages 79-90.
    20. Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "Derivative Security Pricing," Dynamic Modeling and Econometrics in Economics and Finance, Springer, edition 127, number 978-3-662-45906-5, May.

    More about this item

    Keywords

    Marketing;

    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:ags:aaea06:21239. 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: AgEcon Search (email available below). General contact details of provider: https://edirc.repec.org/data/aaeaaea.html .

    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.