TESTING NON-LINEAR DYNAMICS, LONG MEMORY AND CHAOTIC BEHAVIOUR OF ENERGY COMMODITIES
This paper contains a set of tests for nonlinearities in energy commodity prices. The tests comprise both standart diagnostic tests for revealing nonlinearities. The latter test procedures make use of models in chaos theory, so-called long-memory models and some asymmetric adjustment models. Empirical tests are carried out with daily data for crude oil, heating oil, gasoline and natural gas time series covering the period 2010-2015. Test result showed that there are strong nonlinearities in the data. The test for chaos, however, is weak or no existing. The evidence on long memory (in terms of rescaled range and fractional differencing) is somewhat stronger although not very compelling.
 Abarbanel, H.D.I., Brown, R., and Kennel, M. B. 1991. Variations of Lyapunov exponents on a strange attractor, Journal of Nonlinear Science 1: 175-199.
 Abarbanel, H. D. I. 1996 Analysis of Observed Chaotic Data, Springer New York.
 Adrangi, B., and Chatrath, C. 2001. Chaos in oil prices? Evidence from futures market, Energy Economics 23: 405-425.
 Bask, M., and Gençay, R. 1998. Testing chaotic dynamics via Lyapunov exponents, Physica, 114: 1-2.
 Bask, M. 1998. Deterministic chaos in exchange rates? Umeå Economic Studies No 465c, Department of Economics, Umea University, Sweden.
 BenSaida, A. 2015. A practical test for noisy chaotic dynamics, ScienceDirect, Software, X: 3–4, 1–5.
 BenSaida, A. 2014. Noisy chaos in intraday financial data: Evidence from the American index, Applied Mathematics and Computation, 226: 258–65.
 Brock, W., Dechert, W., Scheinkman, J., and LeBaron, B. 1996. A test for independence based on the correlation dimension, Econometric Reviews 15: 197-235.
 Chatrath, A., Adrangi, B., and Dhanda, K. 2002. Are commodity prices chaotic? Agricultural Economics, 27: 123-137.
 Dechert, W., and Gençay, R. 1992. Lyapunov exponents as a nonparametric diagnostic for stability analysis, Journal of Applied Econometrics, 7: S41-S60.
 Dechert, W., and Gençay, R. 2000. Is the largest Lyapunov exponent preserved in embedded dynamics?, Physics Letters A, 276: 59-64.
 Eckmann, J. P., Kamphorst, S. O., Ruelle, D., and Ciliberto, S. 1986. Lyapunov exponents from time series, Physical Review A, 34, 6: 4971-4979.
 Eckmann, J. P., and Ruelle, D. 1985. Ergodic theory of chaos and strange attractors, Reviews of Modern Physics, 57: 617-650.
 Gençay, R., and Dechert, W. 1992. An algorithm for the n Lyapunov exponents of an n-dimensional unknown dynamical system, Physica D, 59: 142-157.
 Gençay, R., and Dechert, W. 1996. The identification of spurious Lyapunov exponents in Jacobian algorithms, Studies in Nonlinear Dynamics and Econometrics, 1: 145-154.
 Gençay, R. 1996. A statistical framework for testing chaotic dynamics via Lyapunov exponents, Physica D, 89: 261-266.
 Grassberger, P., and Procaccia, I. 1983. Characterization of Strange Attractors, Physical Review Letters, 50: 346-394.
 Gunay, S. 2015. Chaotic Structure of the BRIC Countries and Turkey’s Stock Market. International Journal of Economics and Financial Issues, 5(2): 515-522.
 Kantz, H., and Schreiber, T. 2004. Nonlinear time series analysis Cambridge University Press, 2nd edition.
 Panas, E., and Ninni, V. 2000. Are oil markets chaotic? A nonlinear dynamic analysis Energy Economics, 22: 549-568.
 Rosenstein, M., Collins, J.J., and De Luca, C. 1993. A practical method for calculating largest Lyapunov exponents from small data sets, Physica D, 65: 117-134.
 Schuster H. G. 1995. Deterministic Chaos: an introduction, VCH Verlasgesellschaft, Germany.
 The MathWorks, Inc. 2015. MATLAB: The Language of Technical Computing, Natick, Massachusetts, Available at: http://www.mathworks.com/products/matlab.
 Wolf, A., Swift, B., Swinney, and Vastano, J. 1985. Determining Lyapunov exponents from a time series, Physica D, 16: 285-317.
The Copyright Transfer Form to ASERS Publishing (The Publisher)
This form refers to the manuscript, which an author(s) was accepted for publication and was signed by all the authors.
The undersigned Author(s) of the above-mentioned Paper here transfer any and all copyright-rights in and to The Paper to The Publisher. The Author(s) warrants that The Paper is based on their original work and that the undersigned has the power and authority to make and execute this assignment. It is the author's responsibility to obtain written permission to quote material that has been previously published in any form. The Publisher recognizes the retained rights noted below and grants to the above authors and employers for whom the work performed royalty-free permission to reuse their materials below. Authors may reuse all or portions of the above Paper in other works, excepting the publication of the paper in the same form. Authors may reproduce or authorize others to reproduce the above Paper for the Author's personal use or for internal company use, provided that the source and The Publisher copyright notice are mentioned, that the copies are not used in any way that implies The Publisher endorsement of a product or service of an employer, and that the copies are not offered for sale as such. Authors are permitted to grant third party requests for reprinting, republishing or other types of reuse. The Authors may make limited distribution of all or portions of the above Paper prior to publication if they inform The Publisher of the nature and extent of such limited distribution prior there to. Authors retain all proprietary rights in any process, procedure, or article of manufacture described in The Paper. This agreement becomes null and void if and only if the above paper is not accepted and published by The Publisher, or is with drawn by the author(s) before acceptance by the Publisher.