IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Nonlinear and Complex Dynamics in Economics

  • William Barnett

    (Department of Economics, The University of Kansas)

  • Apostolos Serletis

    (Department of Economics, University of Calgary)

  • Demitre Serletis

    (Neurological Institute, Epilepsy Center)

This paper is an up-to-date survey of the state-of-the-art in dynamical systems theory relevant to high levels of dynamical complexity, characterizing chaos and near chaos, as commonly found in the physical sciences. The paper also surveys applications in economics and finance. This survey does not include bifurcation analyses at lower levels of dynamical complexity, such as Hopf and transcritical bifurcations, which arise closer to the stable region of the parameter space. We discuss the geometric approach (based on the theory of differential/difference equations) to dynamical systems and make the basic notions of complexity, chaos, and other related concepts precise, having in mind their (actual or potential) applications to economically motivated questions. We also introduce specific applications in microeconomics, macroeconomics, and finance, and discuss the policy relevancy of chaos.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www2.ku.edu/~kuwpaper/2009Papers/201238.pdf
Download Restriction: no

Paper provided by University of Kansas, Department of Economics in its series WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS with number 201238.

as
in new window

Length: 37 pages
Date of creation: Sep 2012
Date of revision: Sep 2012
Handle: RePEc:kan:wpaper:201238
Contact details of provider: Postal:
415 Snow Hall, Lawrence, KS 66045

Phone: (785) 864-3501
Fax: (785) 864-5270
Web page: http://www2.ku.edu/~kuwpaper/
Email:


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.:

as in new window
  1. Kwiatkowski, D. & Phillips, P.C.B. & Schmidt, P., 1990. "Testing the Null Hypothesis of Stationarity Against the Alternative of Unit Root : How Sure are we that Economic Time Series have a Unit Root?," Papers 8905, Michigan State - Econometrics and Economic Theory.
  2. Baumol, William J & Benhabib, Jess, 1989. "Chaos: Significance, Mechanism, and Economic Applications," Journal of Economic Perspectives, American Economic Association, vol. 3(1), pages 77-105, Winter.
  3. Barnett,William A. & Kirman,Alan P. & Salmon,Mark, 1997. "Nonlinear Dynamics and Economics," Cambridge Books, Cambridge University Press, number 9780521471411, 1.
  4. 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.
  5. 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.
  6. Brock, W.A., 1988. "Nonlinearity And Complex Dynamics In Economics And Finance," Working papers 360, Wisconsin Madison - Social Systems.
  7. Serletis, A. & Gogas, P., 1997. "Chaos in East European Black-Market Exchange Rates," Papers 9708, Calgary - Department of Economics.
  8. 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.
  9. 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.
  10. 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.
  11. Kiminori Matsuyama, 1988. "Endogenous Price Fluctuations in an Optimizing Model of Monetary Economy," Discussion Papers 825, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  12. 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.
  13. Andrew W. Lo & A. Craig MacKinlay, 1987. "Stock Market Prices Do Not Follow Random Walks: Evidence From a Simple Specification Test," NBER Working Papers 2168, National Bureau of Economic Research, Inc.
  14. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
  15. Summers, Lawrence H, 1986. " Does the Stock Market Rationally Reflect Fundamental Values?," Journal of Finance, American Finance Association, vol. 41(3), pages 591-601, July.
  16. 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.
  17. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
  18. Bullard, James & Butler, Alison, 1993. "Nonlinearity and Chaos in Economic Models: Implications for Policy Decisions," Economic Journal, Royal Economic Society, vol. 103(419), pages 849-67, July.
  19. 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.
  20. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
  21. Barnett, William A. & He, Susan, 2010. "Existence of singularity bifurcation in an Euler-equations model of the United States economy: Grandmont was right," Economic Modelling, Elsevier, vol. 27(6), pages 1345-1354, November.
  22. Scheinkman, Jose A, 1990. "Nonlinearities in Economic Dynamics," Economic Journal, Royal Economic Society, vol. 100(400), pages 33-48, Supplemen.
  23. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
  24. Barnett, William A. & Serletis, Apostolos & Serletis, Demitre, 2015. "Nonlinear And Complex Dynamics In Economics," Macroeconomic Dynamics, Cambridge University Press, vol. 19(08), pages 1749-1779, December.
  25. Robert M. Solow, 1956. "A Contribution to the Theory of Economic Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 70(1), pages 65-94.
  26. Jess Benhabib & Richard H. Day, 1981. "Rational Choice and Erratic Behaviour," Review of Economic Studies, Oxford University Press, vol. 48(3), pages 459-471.
  27. Reichlin Pietro, 1997. "Endogenous Cycles in Competitive Models: An Overview," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 1(4), pages 1-13, January.
  28. Day, Richard H, 1982. "Irregular Growth Cycles," American Economic Review, American Economic Association, vol. 72(3), pages 406-14, June.
  29. William Barnett, 2005. "Monetary Aggregation," Macroeconomics 0503017, EconWPA.
  30. 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.
  31. Frank, Murray Z. & Stengos, Thanasis, 1988. "Some evidence concerning macroeconomic chaos," Journal of Monetary Economics, Elsevier, vol. 22(3), pages 423-438.
  32. Banerjee, Sanjibani & Barnett, William A. & Duzhak, Evgeniya A. & Gopalan, Ramu, 2011. "Bifurcation Analysis of Zellner's Marshallain Macroeconomic Model," MPRA Paper 30059, University Library of Munich, Germany.
  33. Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 893-920, October.
  34. 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.
  35. Woodford, Michael, 1986. "Stationary sunspot equilibria in a finance constrained economy," Journal of Economic Theory, Elsevier, vol. 40(1), pages 128-137, October.
  36. 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.
  37. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  38. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
  39. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
  40. Michele Boldrin, 1988. "Paths of Optimal Accumulation in Two-Sector Models," UCLA Economics Working Papers 464, UCLA Department of Economics.
  41. LeRoy, Stephen F, 1989. "Efficient Capital Markets and Martingales," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1583-1621, December.
  42. Hsieh, David A, 1991. " Chaos and Nonlinear Dynamics: Application to Financial Markets," Journal of Finance, American Finance Association, vol. 46(5), pages 1839-77, December.
  43. Nishimura Kazuo & Sorger Gerhard, 1996. "Optimal Cycles and Chaos: A Survey," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 1(1), pages 1-20, April.
  44. 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.
  45. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
  46. Poterba, James M. & Summers, Lawrence H., 1988. "Mean reversion in stock prices : Evidence and Implications," Journal of Financial Economics, Elsevier, vol. 22(1), pages 27-59, October.
  47. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
  48. Reichlin, Pietro, 1986. "Equilibrium cycles in an overlapping generations economy with production," Journal of Economic Theory, Elsevier, vol. 40(1), pages 89-102, October.
  49. Frank, Murray & Gencay, Ramazan & Stengos, Thanasis, 1988. "International chaos?," European Economic Review, Elsevier, vol. 32(8), pages 1569-1584, October.
  50. Serletis, Apostolos, 1995. "Random Walks, Breaking Trend Functions, and the Chaotic Structure of the Velocity of Money," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(4), pages 453-58, October.
  51. Lee, Tae-Hwy & White, Halbert & Granger, Clive W. J., 1993. "Testing for neglected nonlinearity in time series models : A comparison of neural network methods and alternative tests," Journal of Econometrics, Elsevier, vol. 56(3), pages 269-290, April.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:kan:wpaper:201238. 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: (Jianbo Zhang)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.