In Search of Deterministic Complex Patterns in Commodity Prices
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.
Unable to display preview. Download preview PDF.
- 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
- Blank, S.C., 1991, “Chaos” in Futures Markets? A Nonlinear Dynamical Analysis, Journal of Futures Markets, 11, 711–728.Google Scholar
- 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
- Brock, W.A., Dechert, W, and Scheinkman, J., 1987, A Test of Independence Based on the Correlation Dimension, Unpublished Manuscript, University of Wisconsin, Madison, University of Houston, and University of Chicago.Google Scholar
- 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
- Devaney, R.L., 1986, An Introduction to Chaotic Dynamical Systems, Benjamin/Cummings Publishing, Menlo Park, CA.Google Scholar
- Dickey, D.A., and Fuller, W A, Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root, Econometrica, 49, 1057–1072.Google Scholar
- Grassberger, P., and Procaccia, I, 1983, Measuring the Strangeness of Strange Attractors, Physica, 9, 189–208.Google Scholar
- Guckenheimer, J., and Holmes, P, 1986, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag Publishing, New York, NY.Google Scholar
- Nelson, D., 1991, Conditional Heteroskedasticity in Asset Returns: A New Approach, Econometrica, 59, 347–370.Google Scholar
- 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
- Samuelson, P.A., 1965, Proof that Properly Anticipated Prices Fluctuate Randomly, Industrial Management Review, 6, 41–63.Google Scholar
- 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