The Confidence Limits of a Geometric Brownian Motion
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.
|Date of creation:||2006|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: (414) 918-3190
Fax: (414) 276-3349
Web page: http://www.aaea.org
More information through EDIRC
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.:
- 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.
- L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105.
- 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.
- 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.
- 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.
- Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
- Barkoulas, John T. & Baum, Christopher F., 1996.
"Long-term dependence in stock returns,"
Elsevier, vol. 53(3), pages 253-259, December.
- 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, 06.
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
- 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 363-84, March.
- 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 246-73, April.
- 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.
- Comte, F. & Renault, E., 1996. "Long memory continuous time models," Journal of Econometrics, Elsevier, vol. 73(1), pages 101-149, July.
- 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 637-54, May-June.
- 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.
When requesting a correction, please mention this item's handle: RePEc:ags:aaea06:21239. 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: (AgEcon Search)
If references are entirely missing, you can add them using this form.