Advertisement

In Search of Deterministic Complex Patterns in Commodity Prices

  • Arjun Chatrath
  • Bahram Adrangi
  • Kanwalroop K. Dhanda
Part of the Applied Optimization book series (APOP, volume 74)

Abstract

The possibility and implications of chaotic structure in commodity prices is examined. Chaos will imply that prices are deterministic, so that technical rules are more likely to succeed in short run price projections. On the other hand, chaos will necessarily imply that prices are nonlinear and highly sensitive to initial conditions, so that long-term price projections are treacherous. The study conducts tests for the presence of low-dimensional chaotic structure in the futures prices of four important agricultural commodities. Though there is strong evidence of nonlinear dependence, the evidence is not consistent with chaos. The dimension estimates for the commodity futures series are generally much higher than would be for low dimension chaotic series. The test results indicate that ARCH-type processes, with controls for seasonality and contract-maturity effects, explain much of the nonlinearities in the data. The study makes a case that employing seasonally adjusted price series is important in obtaining robust results via some of the existing tests for chaotic structure. Finally, maximum likelihood methodologies, that are robust to the nonlinear dynamics, lend strong support the Samuelson hypothesis of maturity effects in futures price-changes.

Keywords

chaos seasonality 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Akaike, H., 1974, A New Look at Statistical Model Identification, IEEE Transactions on Automatic Control, 19, 716–723.CrossRefGoogle Scholar
  2. Baumol, W.J., and Benhabib, J., 1989, Chaos: Significance, Mechanism, and Economic Applications, Journal of Economic Perspectives, 3, 77–105.CrossRefGoogle Scholar
  3. Benhabib, W.J., and Day, R.H., 1981, Rational Choice and Erratic Behavior, Review of Economic Studies, 48, 459–472.CrossRefGoogle Scholar
  4. Benhabib, W.J., and Day, R.H., 1982, A Characterization of Erratic Dynamics in the Overlapping Generations Model, Journal of Economic Dynamics and Control, 4, 37–55.CrossRefGoogle Scholar
  5. Bessembinder, H., Coughenour, J.F., Seguin, P.J., and Smoller, M.M., 1996, Is there a Term Structure of Futures Volatilities? Reevaluating the Samuelson Hypothesis, Journal of Derivatives, Winter, 45–58.Google Scholar
  6. Blank, S.C., 1991, “Chaos” in Futures Markets? A Nonlinear Dynamical Analysis, Journal of Futures Markets, 11, 711–728.Google Scholar
  7. Bollerslev, T., 1986, Generalized Autoregressive Conditional Heteroskedasticity, Journal of Econometrics, 31, 307–327.CrossRefGoogle Scholar
  8. Brock, W.A., 1986, Distinguishing random and Deterministic Systems, Journal of Economic Theory, 40, 168–195CrossRefGoogle Scholar
  9. Brock, W.A., and Dechert, W., 1988, Theorems on Distinguishing Deterministic and Random Systems, in Barnett, W., Berndt, E., and White, H., Dynamic Econometric Modelling, Proceedings of the Third Austin Symposium, Cambridge: Cambridge University Press.Google Scholar
  10. Brock, W.A., Dechert, W, and Scheinkman, J., 1987, A Test of Independence Based on the Correlation Dimension, Unpublished Manuscript, University of Wisconsin, Madison, University of Houston, and University of Chicago.Google Scholar
  11. Brock, W.A., Hsieh, D.A., and LeBaron, B., 1993, Nonlinear Dynamics, Chaos, and Instability: Statistical Theory and Economic Evidence, MIT Press, Cambridge, Massachusetts.Google Scholar
  12. Brock, W.A., and Sayers, C.L., 1988, Is the Business Cycle Characterized by Deterministic Chaos? Journal of Monetary Economics, 22, 71–90.CrossRefGoogle Scholar
  13. Clyde, W.C., and Osler, C.L., 1997, Charting: Chaos Theory in Disguise? Journal of Futures Markets, 17, 489–514.CrossRefGoogle Scholar
  14. DeCoster, G. P., Labys, W.C., and Mitchell, D.W., 1992, Evidence of Chaos in Commodity Futures Prices, Journal of Futures Markets, 12, 291–305CrossRefGoogle Scholar
  15. Deneckere, R., and Pelikan, S., 1986, Competitive Chaos, Journal of Economic Theory, 40, 12–25.CrossRefGoogle Scholar
  16. Devaney, R.L., 1986, An Introduction to Chaotic Dynamical Systems, Benjamin/Cummings Publishing, Menlo Park, CA.Google Scholar
  17. Dickey, D.A., and Fuller, W A, Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root, Econometrica, 49, 1057–1072.Google Scholar
  18. Engle, R.F., 1982, Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation, Econometrica, 50, 987–1007.CrossRefGoogle Scholar
  19. Frank, M., and Stengos, T., 1989, Measuring the Strangeness of Gold and Silver Rates of Return, Review of Economic Studies, 456, 553–567.CrossRefGoogle Scholar
  20. Grassberger, P., and Procaccia, I, 1983, Measuring the Strangeness of Strange Attractors, Physica, 9, 189–208.Google Scholar
  21. Guckenheimer, J., and Holmes, P, 1986, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag Publishing, New York, NY.Google Scholar
  22. Hsieh, D.A., 1991, Chaos and Nonlinear Dynamics- Applications to Financial Markets, Journal of Finance, 46, 1839–1876.CrossRefGoogle Scholar
  23. Lichtenberg, A.J., and Ujihara, A., 1988, Application of Nonlinear Mapping Theory to Commodity Price Fluctuations, Journal of Economic Dynamics and Control, 13, 225–246.CrossRefGoogle Scholar
  24. Nelson, D., 1991, Conditional Heteroskedasticity in Asset Returns: A New Approach, Econometrica, 59, 347–370.Google Scholar
  25. Nelson, C., and Plosser, C., 1982, Trends and Random Walks in Macroeconomic Time Series, Journal of Monetary Economics, 10, 139–162.CrossRefGoogle Scholar
  26. Rabemananjara, R., and Zakoian, J.M., 1993, Threshold ARCH models and Asymmetries in Volatility, Journal of Applied Econometrics, 8, 31–49.CrossRefGoogle Scholar
  27. Ramsey, J., and Yuan, H., 1987, The Statistical Properties of Dimension Calculations Using Small Data Sets, C. V. Starr Center for Applied Economics, New York University.Google Scholar
  28. Samuelson, P.A., 1965, Proof that Properly Anticipated Prices Fluctuate Randomly, Industrial Management Review, 6, 41–63.Google Scholar
  29. Scheinkman, J., and LeBaron, B., 1989, Nonlinear Dynamics and Stock Returns, Journal of Business, 62, 311–337.CrossRefGoogle Scholar
  30. Stutzer, M.J., 1980, Chaotic Dynamics and Bifurcation in a Macro-Model, Journal of Economic Dynamics and Control, 2, 253–276.CrossRefGoogle Scholar
  31. Takens, F., 1984, On the Numerical Determination of the Dimension of an Attractor, in Dynamical Systems and Bifurcations, Lecture Notes in Mathematics, Springer-Verlag Publishing, Berlin.Google Scholar
  32. Yang, S., and Brorsen, B.W., 1993, Nonlinear Dynamics of Daily Futures Prices: Conditional Heteroskedasticity or Chaos?, Journal of Futures Markets, 13, 175–191.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Arjun Chatrath
    • 1
  • Bahram Adrangi
    • 1
  • Kanwalroop K. Dhanda
    • 1
  1. 1.The Robert B. Pamplin Jr. School of BusinessUniversity of PortlandPortlandUSA

Personalised recommendations