IDEAS home Printed from https://ideas.repec.org/p/fda/fdaddt/2003-09.html
   My bibliography  Save this paper

A New Test for Chaotic Dynamics Using Lyapunov Exponents

Author

Listed:
  • Fernando Fernández-Rodríguez
  • Simón Sosvilla-Rivero
  • Julián Andrada-Félix

Abstract

We propose a new test to detect chaotic dynamics, based on the stability of the largest Lyapunov exponent from different sample sizes. This test is applied to the data used in the single-blind controlled competition tests for nonlinearity and chaos that were generated by Barnett et al. (1997), as well as to several chaotic series. The results suggest that the new test is particularly effective when compared to other stochastic alternatives (both linear and nonlinear). The test size is one for large samples, although for small sample sizes it diminishes below the nominal size for two out of the three chaotic processes considered, what is not a surprise given some well-known properties of such processes.

Suggested Citation

  • Fernando Fernández-Rodríguez & Simón Sosvilla-Rivero & Julián Andrada-Félix, "undated". "A New Test for Chaotic Dynamics Using Lyapunov Exponents," Working Papers 2003-09, FEDEA.
    • Handle: RePEc:fda:fdaddt:2003-09
    as

    Download full text from publisher

    File URL: https://documentos.fedea.net/pubs/dt/2003/dt-2003-09.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. William A. Barnett & A. Ronald Gallant & Melvin J. Hinich & Jochen A. Jungeilges & Daniel T. Kaplan, 2004. "A Single-Blind Controlled Competition Among Tests for Nonlinearity and Chaos," Contributions to Economic Analysis, in: Functional Structure and Approximation in Econometrics, pages 581-615, Emerald Group Publishing Limited.
    2. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
    3. Whang, Yoon-Jae & Linton, Oliver, 1999. "The asymptotic distribution of nonparametric estimates of the Lyapunov exponent for stochastic time series," Journal of Econometrics, Elsevier, vol. 91(1), pages 1-42, July.
    4. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
    5. Bajo-Rubio, Oscar & Fernandez-Rodriguez, Fernando & Sosvilla-Rivero, Simon, 1992. "Chaotic behaviour in exchange-rate series : First results for the Peseta--U.S. dollar case," Economics Letters, Elsevier, vol. 39(2), pages 207-211, June.
    6. Melvin J. Hinich, 1982. "Testing For Gaussianity And Linearity Of A Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 3(3), pages 169-176, May.
    7. Dechert, W D & Gencay, R, 1992. "Lyapunov Exponents as a Nonparametric Diagnostic for Stability Analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages 41-60, Suppl. De.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Simón Sosvilla Rivero & Oscar Bajo Rubio & Carmen Díaz Roldán, "undated". "Sobre la efectividad de la política regional comunitaria: El caso de Castilla-la Mancha," Studies on the Spanish Economy 178, FEDEA.
    2. Simón Sosvilla-Rivero & Fernando Fernández-Rodriguez & Julián Andrada-Félix, 2005. "Testing chaotic dynamics via Lyapunov exponents," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 911-930.
    3. Juan Prieto & Juan Gabriel Rodríguez & Rafael Salas, "undated". "Polarization, Inequality and Tax Reforms," Working Papers 2003-23, FEDEA.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Simón Sosvilla-Rivero & Fernando Fernández-Rodriguez & Julián Andrada-Félix, 2005. "Testing chaotic dynamics via Lyapunov exponents," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 911-930.
    2. Marisa Faggini, 2011. "Chaotic Time Series Analysis in Economics: Balance and Perspectives," Working papers 25, Former Department of Economics and Public Finance "G. Prato", University of Torino.
    3. Kyrtsou, Catherine & Serletis, Apostolos, 2006. "Univariate tests for nonlinear structure," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 154-168, March.
    4. Shintani, Mototsugu & Linton, Oliver, 2004. "Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos," Journal of Econometrics, Elsevier, vol. 120(1), pages 1-33, May.
    5. Mototsugu Shintani & Oliver Linton, 2003. "Is There Chaos in the World Economy? A Nonparametric Test Using Consistent Standard Errors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(1), pages 331-357, February.
    6. Fernandez-Rodriguez, Fernando & Sosvilla-Rivero, Simon, 1998. "Testing nonlinear forecastability in time series: Theory and evidence from the EMS," Economics Letters, Elsevier, vol. 59(1), pages 49-63, April.
    7. Fernandez-Rodriguez, Fernando & Sosvilla-Rivero, Simon & Andrada-Felix, Julian, 1999. "Exchange-rate forecasts with simultaneous nearest-neighbour methods: evidence from the EMS," International Journal of Forecasting, Elsevier, vol. 15(4), pages 383-392, October.
    8. Sandubete, Julio E. & Escot, Lorenzo, 2020. "Chaotic signals inside some tick-by-tick financial time series," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    9. Kyrtsou, Catherine & Malliaris, Anastasios G. & Serletis, Apostolos, 2009. "Energy sector pricing: On the role of neglected nonlinearity," Energy Economics, Elsevier, vol. 31(3), pages 492-502, May.
    10. Herwartz, Helmut & Reimers, Hans-Eggert, 2006. "Modelling the Fisher hypothesis: World wide evidence," Economics Working Papers 2006-04, Christian-Albrechts-University of Kiel, Department of Economics.
    11. Severance-Lossin, E. & Sperlich, S., 1995. "Estimation of Derivatives for Additive Separable Models," SFB 373 Discussion Papers 1995,60, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    12. Hjalmarsson, Erik, 2003. "Does the Black-Scholes formula work for electricity markets? A nonparametric approach," Working Papers in Economics 101, University of Gothenburg, Department of Economics.
    13. Ichimura, Hidehiko & Todd, Petra E., 2007. "Implementing Nonparametric and Semiparametric Estimators," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 74, Elsevier.
    14. Geng, Xin & Janssens, Wendy & Kramer, Berber, 2018. "Liquid milk: Cash Constraints and Recurring Savings among Dairy Farmers in Kenya," 2018 Annual Meeting, August 5-7, Washington, D.C. 273823, Agricultural and Applied Economics Association.
    15. Park, Joon Y. & Whang, Yoon-Jae, 2012. "Random walk or chaos: A formal test on the Lyapunov exponent," Journal of Econometrics, Elsevier, vol. 169(1), pages 61-74.
    16. BERTINELLI, Luisito & STROBL, Eric, 2003. "Urbanization, urban concentration and economic growth in developing countries," LIDAM Discussion Papers CORE 2003076, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    17. Bonsoo Koo & Oliver Linton, 2010. "Semiparametric Estimation of Locally Stationary Diffusion Models," STICERD - Econometrics Paper Series 551, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    18. Zhijie Xiao & Oliver Linton & Raymond J. Carroll & E. Mammen, 2002. "More Efficient Kernel Estimation in Nonparametric Regression with Autocorrelated Errors," Cowles Foundation Discussion Papers 1375, Cowles Foundation for Research in Economics, Yale University.
    19. Dabo-Niang, Sophie & Francq, Christian & Zakoïan, Jean-Michel, 2010. "Combining Nonparametric and Optimal Linear Time Series Predictions," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1554-1565.
    20. Koop, Gary & Poirier, Dale J., 2004. "Bayesian variants of some classical semiparametric regression techniques," Journal of Econometrics, Elsevier, vol. 123(2), pages 259-282, December.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:fda:fdaddt:2003-09. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Carmen Arias (email available below). General contact details of provider: https://www.fedea.net .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.