IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v36y2012i4p670-681.html
   My bibliography  Save this article

The Euro/Dollar exchange rate: Chaotic or non-chaotic? A continuous time model with heterogeneous beliefs

Author

Listed:
  • Federici, Daniela
  • Gandolfo, Giancarlo

Abstract

The aim of this paper is to develop a continuous time exchange rate model that allows for heterogeneity of the agents' beliefs, in order to explore non-linearities and possible chaotic behaviour. The theoretical model contains an intrinsic non-linearity that gives rise to a jerk differential equation, which is in principle capable of generating chaos. The model is econometrically estimated in continuous time with Euro/Dollar data and examined for the possible presence of chaotic motion. Our results indicate that the possibility of chaotic dynamics in our model is rejected.

Suggested Citation

  • Federici, Daniela & Gandolfo, Giancarlo, 2012. "The Euro/Dollar exchange rate: Chaotic or non-chaotic? A continuous time model with heterogeneous beliefs," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 670-681.
    • Handle: RePEc:eee:dyncon:v:36:y:2012:i:4:p:670-681
    DOI: 10.1016/j.jedc.2011.11.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165188911002223
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jedc.2011.11.008?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jerome L. Stein, 2002. "Enlargement and the Value of the Euro," Australian Economic Papers, Wiley Blackwell, vol. 41(4), pages 462-479, December.
    2. Day, Richard H. & Huang, Weihong, 1990. "Bulls, bears and market sheep," Journal of Economic Behavior & Organization, Elsevier, vol. 14(3), pages 299-329, December.
    3. Carl Chiarella & Roberto Dieci & Xue-Zhong He, 2008. "Heterogeneity, Market Mechanisms, and Asset Price Dynamics," Research Paper Series 231, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Michel Beine & Paul De Grauwe & Marianna Grimaldi, 2014. "The Impact of FX Central Bank Intervention in a Noise Trading Framework," World Scientific Book Chapters, in: Exchange Rates and Global Financial Policies, chapter 6, pages 189-216, World Scientific Publishing Co. Pte. Ltd..
    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. Richard Meese & Kenneth Rogoff, 1983. "The Out-of-Sample Failure of Empirical Exchange Rate Models: Sampling Error or Misspecification?," NBER Chapters, in: Exchange Rates and International Macroeconomics, pages 67-112, National Bureau of Economic Research, Inc.
    7. Belloc, Marianna & Federici, Daniela, 2010. "A two-country NATREX model for the euro/dollar," Journal of International Money and Finance, Elsevier, vol. 29(2), pages 315-335, March.
    8. Scheinkman, Jose A & LeBaron, Blake, 1989. "Nonlinear Dynamics and Stock Returns," The Journal of Business, University of Chicago Press, vol. 62(3), pages 311-337, July.
    9. Gaunersdorfer, Andrea & Hommes, Cars H. & Wagener, Florian O.O., 2008. "Bifurcation routes to volatility clustering under evolutionary learning," Journal of Economic Behavior & Organization, Elsevier, vol. 67(1), pages 27-47, July.
    10. Sebastian Edwards, 2005. "Is the U.S. Current Account Deficit Sustainable? And If Not, How Costly is Adjustment Likely To Be?," NBER Working Papers 11541, National Bureau of Economic Research, Inc.
    11. J. Barkley Rosser Jr. (ed.), 2009. "Handbook of Research on Complexity," Books, Edward Elgar Publishing, number 3625.
    12. 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.
    13. Paul De Grauwe & Marianna Grimaldi, 2014. "Exchange Rate Puzzles: A Tale of Switching Attractors," World Scientific Book Chapters, in: Exchange Rates and Global Financial Policies, chapter 3, pages 71-117, World Scientific Publishing Co. Pte. Ltd..
    14. Frankel, Jeffrey A & Froot, Kenneth A, 1987. "Using Survey Data to Test Standard Propositions Regarding Exchange Rate Expectations," American Economic Review, American Economic Association, vol. 77(1), pages 133-153, March.
    15. Stein, Jerome L., 2006. "Stochastic Optimal Control, International Finance, and Debt Crises," OUP Catalogue, Oxford University Press, number 9780199280575, Decembrie.
    16. Hens, Thorsten & Schenk-Hoppe, Klaus Reiner (ed.), 2009. "Handbook of Financial Markets: Dynamics and Evolution," Elsevier Monographs, Elsevier, edition 1, number 9780123742582.
    17. Boswijk, H. Peter & Hommes, Cars H. & Manzan, Sebastiano, 2007. "Behavioral heterogeneity in stock prices," Journal of Economic Dynamics and Control, Elsevier, vol. 31(6), pages 1938-1970, June.
    18. Giancarlo Gandolfo & Pier Carlo Padoan & Giuseppe Arcangelis, 1993. "The Theory of Exchange Rate Determination, and Exchange Rate Forecasting," International Economic Association Series, in: Helmut Frisch & Andreas Wörgötter (ed.), Open-Economy Macroeconomics, chapter 18, pages 332-352, Palgrave Macmillan.
    19. Bask, Mikael, 2000. "A Positive Lyapunov Exponent in Swedish Exchange Rates?," Umeå Economic Studies 528, Umeå University, Department of Economics.
    20. Paul Grauwe & Hans Dewachter, 1993. "A chaotic model of the exchange rate: The role of fundamentalists and chartists," Open Economies Review, Springer, vol. 4(4), pages 351-379, December.
    21. Michel Beine & Jérôme Lahaye & Sébastien Laurent & Christopher J. Neely & Franz C. Palm, 2007. "Central bank intervention and exchange rate volatility, its continuous and jump components," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 12(2), pages 201-223.
    22. Daniela Federici & Giancarlo Gandolfo, 2001. "Chaos and the exchange rate," The Journal of International Trade & Economic Development, Taylor & Francis Journals, vol. 11(2), pages 111-142.
    23. Wymer, C R, 1972. "Econometric Estimation of Stochastic Differential Equation Systems," Econometrica, Econometric Society, vol. 40(3), pages 565-577, May.
    24. Giancarlo Gandolfo, 2016. "International Finance and Open-Economy Macroeconomics," Springer Texts in Business and Economics, Springer, edition 2, number 978-3-662-49862-0, August.
    25. Wymer, Clifford R., 1997. "Structural Nonlinear Continuous-Time Models In Econometrics," Macroeconomic Dynamics, Cambridge University Press, vol. 1(2), pages 518-548, June.
    26. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    27. Paul Grauwe & Hans Dewachter, 1993. "A Chaotic Monetary Model of the Exchange Rate," International Economic Association Series, in: Helmut Frisch & Andreas Wörgötter (ed.), Open-Economy Macroeconomics, chapter 19, pages 353-376, Palgrave Macmillan.
    28. Gandolfo, Giancarlo & Padoan, Pietro Carlo & Paladino, Giovanna, 1990. "Exchange rate determination: Single-equation or economy-wide models? : A test against the random walk," Journal of Banking & Finance, Elsevier, vol. 14(5), pages 965-992, November.
    29. Dominguez, Kathryn M.E., 2006. "When do central bank interventions influence intra-daily and longer-term exchange rate movements?," Journal of International Money and Finance, Elsevier, vol. 25(7), pages 1051-1071, November.
    30. Meese, Richard A. & Rogoff, Kenneth, 1983. "Empirical exchange rate models of the seventies : Do they fit out of sample?," Journal of International Economics, Elsevier, vol. 14(1-2), pages 3-24, February.
    31. Jerome L. Stein, 2001. "The Equilibrium Value of the Euro/$ US Exchange Rate: An Evaluation of Research," CESifo Working Paper Series 525, CESifo.
    32. Frankel, Jeffrey A & Froot, Kenneth A, 1990. "Chartists, Fundamentalists, and Trading in the Foreign Exchange Market," American Economic Review, American Economic Association, vol. 80(2), pages 181-185, May.
    33. LeBaron, Blake & Arthur, W. Brian & Palmer, Richard, 1999. "Time series properties of an artificial stock market," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1487-1516, September.
    34. Brzozowska-Rup, Katarzyna & Orłowski, Arkadiusz, 2004. "Application of bootstrap to detecting chaos in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 317-321.
    35. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186, Elsevier.
    36. John Creedy & Vance L. Martin (ed.), 1994. "Chaos and Non-Linear Models in Economics," Books, Edward Elgar Publishing, number 116.
    37. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August.
    38. Lux, Thomas, 1998. "The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions," Journal of Economic Behavior & Organization, Elsevier, vol. 33(2), pages 143-165, January.
    39. Kenneth S. Rogoff & Vania Stavrakeva, 2008. "The Continuing Puzzle of Short Horizon Exchange Rate Forecasting," NBER Working Papers 14071, National Bureau of Economic Research, Inc.
    40. De Grauwe, Paul, 1990. "Deterministic Chaos in the Foreign Exchange Markets," CEPR Discussion Papers 370, C.E.P.R. Discussion Papers.
    41. Mr. Jerome L. Stein, 1995. "The Fundamental Determinants of the Real Exchange Rate of the U. S. Dollar Relative to Other G-7 Currencies," IMF Working Papers 1995/081, International Monetary Fund.
    42. Owen F. Humpage, 2003. "Government intervention in the foreign exchange market," Working Papers (Old Series) 0315, Federal Reserve Bank of Cleveland.
    43. William A. Brock & Cars H. Hommes, 2001. "A Rational Route to Randomness," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 16, pages 402-438, Edward Elgar Publishing.
    44. Stein, Jerome L., 1990. "The real exchange rate," Journal of Banking & Finance, Elsevier, vol. 14(5), pages 1045-1078, November.
    45. Sergio Da Silva, 2001. "Chaotic Exchange Rate Dynamics Redux," Open Economies Review, Springer, vol. 12(3), pages 281-304, July.
    46. Resende, Marcelo & Zeidan, Rodrigo M., 2008. "Expectations and chaotic dynamics: Empirical evidence on exchange rates," Economics Letters, Elsevier, vol. 99(1), pages 33-35, April.
    47. Buti,Marco & Deroose,Servaas & Gaspar,Vitor & Martins,João Nogueira (ed.), 2010. "The Euro," Cambridge Books, Cambridge University Press, number 9789279098420.
    48. Lillie Lam & Laurence Fung & Ip-wing Yu, 2008. "Comparing Forecast Performance of Exchange Rate Models," Working Papers 0808, Hong Kong Monetary Authority.
    49. Marianna Belloc & Daniela Federici & Giancarlo Gandolfo, 2008. "The Euro/Dollar Equilibrium Real Exchange Rate: A Continuous Time Approach," Economia politica, Società editrice il Mulino, issue 2, pages 243-264.
    50. Brooks, Chris, 1998. "Chaos in Foreign Exchange Markets: A Sceptical View," Computational Economics, Springer;Society for Computational Economics, vol. 11(3), pages 265-281, June.
    51. Crespo Cuaresma, Jesus, 1998. "Deterministic Chaos versus Stochastic Processes," Economics Series 60, Institute for Advanced Studies.
    52. Wymer, Clifford R., 2009. "Aperiodic Dynamics In The Bergstrom/Wymer Model Of The United Kingdom," Econometric Theory, Cambridge University Press, vol. 25(4), pages 1099-1111, August.
    53. Chen, Shikuan, 1999. "Complex Dynamics of the Real Exchange Rate in an Open Macroeconomic Model," Journal of Macroeconomics, Elsevier, vol. 21(3), pages 493-508, July.
    54. Szpiro, George G., 1994. "Exchange rate speculation and chaos inducing intervention," Journal of Economic Behavior & Organization, Elsevier, vol. 24(3), pages 363-368, August.
    55. Sebastian Edwards, 2005. "Is the U.S. Current Account Deficit Sustainable? If Not, How Costly Is Adjustment Likely to Be?," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 36(1), pages 211-288.
    56. Serletis, Apostolos & Shahmoradi, Asghar, 2004. "ABSENCE OF CHAOS AND 1/f SPECTRA, BUT EVIDENCE OF TAR NONLINEARITIES, IN THE CANADIAN EXCHANGE RATE," Macroeconomic Dynamics, Cambridge University Press, vol. 8(04), pages 543-551, September.
    57. Jeffrey A. Frankel & Kenneth A. Froot, 1985. "Using Survey Data to Test Some Standard Propositions Regarding Exchange Rate Expectations," NBER Working Papers 1672, National Bureau of Economic Research, Inc.
    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. Mignot, Sarah & Westerhoff, Frank H., 2023. "Explaining the stylized facts of foreign exchange markets with a simple agent-based version of Paul de Grauwe's chaotic exchange rate model," BERG Working Paper Series 189, Bamberg University, Bamberg Economic Research Group.
    2. Kohler, Karsten, 2019. "Exchange rate dynamics, balance sheet effects, and capital flows. A Minskyan model of emerging market boom-bust cycles," Structural Change and Economic Dynamics, Elsevier, vol. 51(C), pages 270-283.
    3. Zouhaier Dhifaoui, 2022. "Determinism and Non-linear Behaviour of Log-return and Conditional Volatility: Empirical Analysis for 26 Stock Markets," South Asian Journal of Macroeconomics and Public Finance, , vol. 11(1), pages 69-94, June.
    4. Giancarlo Gandolfo, 2015. "The Tobin tax in a continuous-time non-linear dynamic model of the exchange rate," Cambridge Journal of Economics, Cambridge Political Economy Society, vol. 39(6), pages 1629-1643.
    5. Chen, Xiaoshan & MacDonald, Ronald, 2014. "Measuring the Euro-Dollar Permanent Equilibrium Exchange Rate using the Unobserved Components Model," SIRE Discussion Papers 2015-05, Scottish Institute for Research in Economics (SIRE).
    6. Michele Gori & Giorgio Ricchiuti, 2018. "A dynamic exchange rate model with heterogeneous agents," Journal of Evolutionary Economics, Springer, vol. 28(2), pages 399-415, April.
    7. Chen, Xiaoshan & MacDonald, Ronald, 2014. "Measuring the Euro-Dollar Permanent Equilibrium Exchange Rate using the Unobserved Components Model," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-05, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    8. Chen, Xiaoshan & MacDonald, Ronald, 2015. "Measuring the dollar–euro permanent equilibrium exchange rate using the unobserved components model," Journal of International Money and Finance, Elsevier, vol. 53(C), pages 20-35.

    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. Daniela Federici & Giancarlo Gandolfo, 2011. "The Euro/Dollar Exchange Rate: Chaotic or Non-Chaotic?," CESifo Working Paper Series 3420, CESifo.
    2. Chiarella, Carl & He, Xue-Zhong & Zwinkels, Remco C.J., 2014. "Heterogeneous expectations in asset pricing: Empirical evidence from the S&P500," Journal of Economic Behavior & Organization, Elsevier, vol. 105(C), pages 1-16.
    3. Xue-Zhong He & Youwei Li, 2017. "The adaptiveness in stock markets: testing the stylized facts in the DAX 30," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 1071-1094, November.
    4. Dick, Christian D. & Menkhoff, Lukas, 2013. "Exchange rate expectations of chartists and fundamentalists," Journal of Economic Dynamics and Control, Elsevier, vol. 37(7), pages 1362-1383.
    5. Frijns, Bart & Lehnert, Thorsten & Zwinkels, Remco C.J., 2010. "Behavioral heterogeneity in the option market," Journal of Economic Dynamics and Control, Elsevier, vol. 34(11), pages 2273-2287, November.
    6. Cars Hommes & Florian Wagener, 2008. "Complex Evolutionary Systems in Behavioral Finance," Tinbergen Institute Discussion Papers 08-054/1, Tinbergen Institute.
    7. Jongen, Ron & Verschoor, Willem F.C. & Wolff, Christian C.P. & Zwinkels, Remco C.J., 2012. "Explaining dispersion in foreign exchange expectations: A heterogeneous agent approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(5), pages 719-735.
    8. Zheng, Min & Wang, Hefei & Wang, Chengzhang & Wang, Shouyang, 2017. "Speculative behavior in a housing market: Boom and bust," Economic Modelling, Elsevier, vol. 61(C), pages 50-64.
    9. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186, Elsevier.
    10. Hommes, Cars & Kiseleva, Tatiana & Kuznetsov, Yuri & Verbic, Miroslav, 2012. "Is More Memory In Evolutionary Selection (De)Stabilizing?," Macroeconomic Dynamics, Cambridge University Press, vol. 16(3), pages 335-357, June.
    11. Raquel Almeida Ramos & Federico Bassi & Dany Lang, 2020. "Bet against the trend and cash in profits," CEPN Working Papers halshs-02956879, HAL.
    12. Tramontana, Fabio & Westerhoff, Frank & Gardini, Laura, 2015. "A simple financial market model with chartists and fundamentalists: Market entry levels and discontinuities," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 16-40.
    13. Saskia ter Ellen & Willem F.C. Verschoor, 2017. "Heterogeneous beliefs and asset price dynamics: a survey of recent evidence," Working Paper 2017/22, Norges Bank.
    14. Menkhoff, Lukas & Rebitzky, Rafael R. & Schröder, Michael, 2009. "Heterogeneity in exchange rate expectations: Evidence on the chartist-fundamentalist approach," Journal of Economic Behavior & Organization, Elsevier, vol. 70(1-2), pages 241-252, May.
    15. Chiarella, Carl & He, Xue-Zhong & Zheng, Min, 2011. "An analysis of the effect of noise in a heterogeneous agent financial market model," Journal of Economic Dynamics and Control, Elsevier, vol. 35(1), pages 148-162, January.
    16. Schmitt, Noemi, 2018. "Heterogeneous expectations and asset price dynamics," BERG Working Paper Series 134, Bamberg University, Bamberg Economic Research Group.
    17. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    18. Alexandru Mandes & Peter Winker, 2017. "Complexity and model comparison in agent based modeling of financial markets," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 12(3), pages 469-506, October.
    19. Brock, W.A. & Hommes, C.H. & Wagener, F.O.O., 2009. "More hedging instruments may destabilize markets," Journal of Economic Dynamics and Control, Elsevier, vol. 33(11), pages 1912-1928, November.
    20. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.

    More about this item

    Keywords

    Exchange rate; Chaos; Jerk equation; Continuous time econometrics;
    All these keywords.

    JEL classification:

    • F31 - International Economics - - International Finance - - - Foreign Exchange
    • F37 - International Economics - - International Finance - - - International Finance Forecasting and Simulation: Models and Applications
    • C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    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:eee:dyncon:v:36:y:2012:i:4:p:670-681. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jedc .

    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.