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Martingales, Nonlinearity, And Chaos

  • William Barnett

    (Department of Economics, The University of Kansas)

  • Apostolos Serletis

    (Department of Economics, The University of Calgary)

In this article we provide a review of the literature with respect to the efficient markets hypothesis and chaos. In doing so, we contrast the martingale behavior of asset prices to nonlinear chaotic dynamics, discuss some recent techniques used in distinguishing between probabilistic and deterministic behavior in asset prices, and report some evidence. Moreover, we look at the controversies that have arisen about the available tests and results, and raise the issue of whether dynamical systems theory is practical in finance.

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File URL: http://www2.ku.edu/~kuwpaper/2009Papers/201225.pdf
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Paper provided by University of Kansas, Department of Economics in its series WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS with number 201225.

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Length: 28 pages
Date of creation: Sep 2012
Date of revision: Sep 2012
Handle: RePEc:kan:wpaper:201225
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  1. James M. Poterba & Lawrence H. Summers, 1987. "Mean Reversion in Stock Prices: Evidence and Implications," NBER Working Papers 2343, National Bureau of Economic Research, Inc.
  2. Ramsey, J.B. & Sayers, C.L. & Rothman, P., 1988. "The Statistical Properties Of Dimension Calculations Using Small Data Sets: Some Economic Applications," Papers 15, Houston - Department of Economics.
  3. Frank, Murray & Gencay, Ramazan & Stengos, Thanasis, 1988. "International chaos?," European Economic Review, Elsevier, vol. 32(8), pages 1569-1584, October.
  4. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
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  7. LeRoy, Stephen F, 1989. "Efficient Capital Markets and Martingales," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1583-1621, December.
  8. Ramsey, James B & Rothman, Philip, 1994. "Nonlinear Monetary Dynamics: Comment," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(1), pages 135-36, January.
  9. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
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  11. Abhyankar, A & Copeland, L S & Wong, W, 1997. "Uncovering Nonlinear Structure in Real-Time Stock-Market Indexes: The S&P 500, the DAX, the Nikkei 225, and the FTSE-100," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 1-14, January.
  12. Barnett, William A. & Gallant, A. Ronald & Hinich, Melvin J. & Jungeilges, Jochen A. & Kaplan, Daniel T. & Jensen, Mark J., 1997. "A single-blind controlled competition among tests for nonlinearity and chaos," Journal of Econometrics, Elsevier, vol. 82(1), pages 157-192.
  13. DeCoster, Gregory P & Mitchell, Douglas W, 1991. "Nonlinear Monetary Dynamics," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 455-61, October.
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  15. William Barnett, 2005. "Monetary Aggregation," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200510, University of Kansas, Department of Economics, revised Mar 2005.
  16. Grandmont Jean-michel, 1983. "On endogenous competitive business cycles," CEPREMAP Working Papers (Couverture Orange) 8316, CEPREMAP.
  17. Granger, Clive W J, 1995. "Modelling Nonlinear Relationships between Extended-Memory Variables," Econometrica, Econometric Society, vol. 63(2), pages 265-79, March.
  18. Scheinkman, Jose A & LeBaron, Blake, 1989. "Nonlinear Dynamics and Stock Returns," The Journal of Business, University of Chicago Press, vol. 62(3), pages 311-37, July.
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  21. repec:gue:guelph:1988-15 is not listed on IDEAS
  22. Frank, Murray Z. & Stengos, Thanasis, 1988. "Some evidence concerning macroeconomic chaos," Journal of Monetary Economics, Elsevier, vol. 22(3), pages 423-438.
  23. 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.
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  25. Brock, William A. & Sayers, Chera L., 1988. "Is the business cycle characterized by deterministic chaos?," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 71-90, July.
  26. Abhyankar, A & Copeland, L S & Wong, W, 1995. "Nonlinear Dynamics in Real-Time Equity Market Indices: Evidence from the United Kingdom," Economic Journal, Royal Economic Society, vol. 105(431), pages 864-80, July.
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  29. Serletis, A. & Gogas, P., 1997. "Chaos in East European Black-Market Exchange Rates," Papers 9708, Calgary - Department of Economics.
  30. Scheinkman, Jose A, 1990. "Nonlinearities in Economic Dynamics," Economic Journal, Royal Economic Society, vol. 100(400), pages 33-48, Supplemen.
  31. Murray Frank & Thanasis Stengos, 1989. "Measuring the Strangeness of Gold and Silver Rates of Return," Review of Economic Studies, Oxford University Press, vol. 56(4), pages 553-567.
  32. Barnett, William A. & Ronald Gallant, A. & Hinich, Melvin J. & Jungeilges, Jochen A. & Kaplan, Daniel T. & Jensen, Mark J., 1995. "Robustness of nonlinearity and chaos tests to measurement error, inference method, and sample size," Journal of Economic Behavior & Organization, Elsevier, vol. 27(2), pages 301-320, July.
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