[go: up one dir, main page]

IDEAS home Printed from https://ideas.repec.org/p/tur/wpaper/25.html
   My bibliography  Save this paper

Chaotic Time Series Analysis in Economics: Balance and Perspectives

Author

Listed:
  • Marisa Faggini

    (Department of Economics and Statistics, University of Salerno)

Abstract
To show that a mathematical model exhibits chaotic behaviour does not prove that chaos is also present in the corresponding data. To convincingly show that a system behaves chaotically, chaos has to be identified directly from the data. From an empirical point of view, it is difficult to distinguish between fluctuations provoked by random shocks and endogenous fluctuations determined by the nonlinear nature of the relation between economic aggregates. For this purpose, chaos tests test are developed to investigate the basic features of chaotic phenomena: nonlinearity, fractal attractor, and sensitivity to initial conditions. The aim of the paper is not to review the large body of work concerning nonlinear time series analysis in economics, about which much has been written, but rather to focus on the new techniques developed to detect chaotic behaviours in the data. More specifically, our attention will be devoted to reviewing the results reached by the application of these techniques to economic and financial time series and to understand why chaos theory, after a period of growing interest, appears now not to be such an interesting and promising research area.

Suggested Citation

  • 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.
  • Handle: RePEc:tur:wpaper:25
    as

    Download full text from publisher

    File URL: http://www.bemservizi.unito.it/repec/tur/wpaper/n25.pdf
    File Function: First version, 2011
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Stutzer, Michael J., 1980. "Chaotic dynamics and bifurcation in a macro model," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 353-376, May.
    2. Serletis, Apostolos & Shintani, Mototsugu, 2006. "Chaotic monetary dynamics with confidence," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 228-252, March.
    3. 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.
    4. William A. Barnett & A. Ronald Gallant & Melvin J. Hinich & Jochen A. Jungeilges & Daniel T. Kaplan, 2004. "Robustness of Nonlinearity and Chaos Tests to Measurement Error, Inference Method, and Sample Size," Contributions to Economic Analysis, in: Functional Structure and Approximation in Econometrics, pages 529-548, Emerald Group Publishing Limited.
    5. Barnett, William A., 2006. "Comments on "Chaotic monetary dynamics with confidence"," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 253-255, March.
    6. Mizrach, Bruce, 1996. "Determining delay times for phase space reconstruction with application to the FF/DM exchange rate," Journal of Economic Behavior & Organization, Elsevier, vol. 30(3), pages 369-381, September.
    7. Belaire-Franch, Jorge & Contreras, Dulce, 2002. "Recurrence Plots in Nonlinear Time Series Analysis: Free Software," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 7(i09).
    8. 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.
    9. 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.
    10. M. Matilla-GarcÍa & R. Queralt & P. Sanz & F. VÁzquez, 2004. "A Generalized BDS Statistic," Computational Economics, Springer;Society for Computational Economics, vol. 24(3), pages 277-300, September.
    11. 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.
    12. William A. Barnett & Yijun He, 2000. "Unsolved Econometric Problems in Nonlinearity, Chaos, and Bifurcation," Macroeconomics 0004021, University Library of Munich, Germany.
    13. Barnett, William A. & Serletis, Apostolos, 2000. "Martingales, nonlinearity, and chaos," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 703-724, June.
    14. Antoniou, Antonios & Vorlow, Constantinos E., 2005. "Price clustering and discreteness: is there chaos behind the noise?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 348(C), pages 389-403.
    15. Bastos, João A. & Caiado, Jorge, 2011. "Recurrence quantification analysis of global stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(7), pages 1315-1325.
    16. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    17. Deneckere, Raymond & Pelikan, Steve, 1986. "Competitive chaos," Journal of Economic Theory, Elsevier, vol. 40(1), pages 13-25, October.
    18. Frank, Murray Z. & Stengos, Thanasis, 1988. "Some evidence concerning macroeconomic chaos," Journal of Monetary Economics, Elsevier, vol. 22(3), pages 423-438.
    19. Gilmore, Claire G., 2001. "An examination of nonlinear dependence in exchange rates, using recent methods from chaos theory," Global Finance Journal, Elsevier, vol. 12(1), pages 139-151.
    20. 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.
    21. Serletis, Apostolos & Gogas, Periklis, 1997. "Chaos in East European black market exchange rates," Research in Economics, Elsevier, vol. 51(4), pages 359-385, December.
    22. Steven C. Blank, 1991. "“Chaos” in futures markets? A nonlinear dynamical analysis," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 11(6), pages 711-728, December.
    23. Frank, Murray Z & Stengos, Thanasis, 1988. "Chaotic Dynamics in Economic Time-Series," Journal of Economic Surveys, Wiley Blackwell, vol. 2(2), pages 103-133.
    24. Strozzi, Fernanda & Zaldı́var, José-Manuel & Zbilut, Joseph P, 2002. "Application of nonlinear time series analysis techniques to high-frequency currency exchange data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(3), pages 520-538.
    25. William Barnett, 2005. "Monetary Aggregation," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200510, University of Kansas, Department of Economics, revised Mar 2005.
    26. Brock, W. A., 1986. "Distinguishing random and deterministic systems: Abridged version," Journal of Economic Theory, Elsevier, vol. 40(1), pages 168-195, October.
    27. Granger, Clive W.J., 2001. "Overview Of Nonlinear Macroeconometric Empirical Models," Macroeconomic Dynamics, Cambridge University Press, vol. 5(4), pages 466-481, September.
    28. DeCoster, Gregory P & Mitchell, Douglas W, 1991. "Nonlinear Monetary Dynamics," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 455-461, October.
    29. Marcus A. Streips, 1995. "The Problem of the Persistent Hog Price Cycle: A Chaotic Solution," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 77(5), pages 1397-1403.
    30. Ramsey, James B & Sayers, Chera L & Rothman, Philip, 1990. "The Statistical Properties of Dimension Calculations Using Small Data Sets: Some Economic Applications," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(4), pages 991-1020, November.
    31. Anning Wei & Raymond M. Leuthold, 1998. "Long Agricultural Futures Prices: ARCH, Long Memory, or Chaos Processes?," Finance 9805001, University Library of Munich, Germany.
    32. Bask, Mikael, 2000. "A Positive Lyapunov Exponent in Swedish Exchange Rates?," Umeå Economic Studies 528, Umeå University, Department of Economics.
    33. Gilmore, Claire G., 1993. "A new test for chaos," Journal of Economic Behavior & Organization, Elsevier, vol. 22(2), pages 209-237, October.
    34. 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.
    35. Ravi Vaidyanathan & Tim Krehbiel, 1992. "Does the S&P 500 futures mispricing series exhibit nonlinear dependence across time?," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 12(6), pages 659-677, December.
    36. 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.
    37. Richard H. Day, 1994. "Complex Economic Dynamics - Vol. 1: An Introduction to Dynamical Systems and Market Mechanisms," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262041413, April.
    38. Claire G. Gilmore, 1996. "Detecting Linear and Nonlinear Dependence in Stock Returns: New Methods Derived from Chaos Theory," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 23(9-10), pages 1357-1377, December.
    39. Day, Richard H, 1982. "Irregular Growth Cycles," American Economic Review, American Economic Association, vol. 72(3), pages 406-414, June.
    40. Seung‐Ryong Yang & B. Wade Brorsen, 1993. "Nonlinear dynamics of daily futures prices: Conditional heteroskedasticity or chaos?," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 13(2), pages 175-191, April.
    41. Jorge Belaire-Franch, & Dulce Contreras & Lorena Tordera-Lledo, 2002. "Assessing Non-Linear Structures in Real Exchange Rates Using Recurrence Plot Strategies," Computing in Economics and Finance 2002 239, Society for Computational Economics.
    42. Hsieh, David A., 1993. "Using non-linear methods to search for risk premia in currency futures," Journal of International Economics, Elsevier, vol. 35(1-2), pages 113-132, August.
    43. de Lima, Pedro J F, 1998. "Nonlinearities and Nonstationarities in Stock Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 227-236, April.
    44. Jess Benhabib & Richard H. Day, 1981. "Rational Choice and Erratic Behaviour," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(3), pages 459-471.
    45. Adrangi, Bahram & Chatrath, Arjun & Dhanda, Kanwalroop Kathy & Raffiee, Kambiz, 2001. "Chaos in oil prices? Evidence from futures markets," Energy Economics, Elsevier, vol. 23(4), pages 405-425, July.
    46. Nowrouz Kohzadi & Milton S. Boyd, 1995. "Testing for Chaos and Nonlinear Dynamics in Cattle Prices," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 43(3), pages 475-484, November.
    47. Murray Frank & Thanasis Stengos, 1989. "Measuring the Strangeness of Gold and Silver Rates of Return," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(4), pages 553-567.
    48. Barkoulas, John T., 2008. "Testing for deterministic monetary chaos: Metric and topological diagnostics," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1013-1024.
    49. B. Wade Brorsen & Seung-Ryong Yang, 1994. "Nonlinear Dynamics And The Distribution Of Daily Stock Index Returns," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 17(2), pages 187-203, June.
    50. Seung-Ryong Yang & B. Wade Brorsen, 1992. "Nonlinear Dynamics of Daily Cash Prices," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 74(3), pages 706-715.
    51. John Barkoulas & Nickolaos Travlos, 1998. "Chaos in an emerging capital market? The case of the Athens Stock Exchange," Applied Financial Economics, Taylor & Francis Journals, vol. 8(3), pages 231-243.
    52. McKenzie, Michael D., 2001. "Chaotic behavior in national stock market indices: New evidence from the close returns test," Global Finance Journal, Elsevier, vol. 12(1), pages 35-53.
    53. Catherine Kyrtsou & Walter C. Labys & Michel Terraza, 2004. "Noisy chaotic dynamics in commodity markets," Empirical Economics, Springer, vol. 29(3), pages 489-502, September.
    54. Panas, Epaminondas & Ninni, Vassilia, 2000. "Are oil markets chaotic? A non-linear dynamic analysis," Energy Economics, Elsevier, vol. 22(5), pages 549-568, October.
    55. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    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. Emilian Lucian NEACSU & Marcela Daniela TODONI, 2014. "A Way To Determine Chaotic Behaviour In Romanian Stock Market," Review of Economic and Business Studies, Alexandru Ioan Cuza University, Faculty of Economics and Business Administration, issue 14, pages 207-214, December.
    2. Rachida Hennani, 2015. "Can the Lasota(1977)’s model compete with the Mackey-Glass(1977)’s model in nonlinear modelling of financial time series?," Working Papers 15-09, LAMETA, Universtiy of Montpellier, revised Jun 2015.

    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. Marisa Faggini & Bruna Bruno & Anna Parziale, 2019. "Does Chaos Matter in Financial Time Series Analysis?," International Journal of Economics and Financial Issues, Econjournals, vol. 9(4), pages 18-24.
    2. Barnett, William A. & Serletis, Apostolos & Serletis, Demitre, 2015. "Nonlinear And Complex Dynamics In Economics," Macroeconomic Dynamics, Cambridge University Press, vol. 19(8), pages 1749-1779, December.
    3. McKenzie, Michael D., 2001. "Chaotic behavior in national stock market indices: New evidence from the close returns test," Global Finance Journal, Elsevier, vol. 12(1), pages 35-53.
    4. Barnett, William A. & Serletis, Apostolos, 2000. "Martingales, nonlinearity, and chaos," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 703-724, June.
    5. Adrangi, Bahram & Chatrath, Arjun & Dhanda, Kanwalroop Kathy & Raffiee, Kambiz, 2001. "Chaos in oil prices? Evidence from futures markets," Energy Economics, Elsevier, vol. 23(4), pages 405-425, July.
    6. Olmedo, Elena, 2011. "Is there chaos in the Spanish labour market?," Chaos, Solitons & Fractals, Elsevier, vol. 44(12), pages 1045-1053.
    7. Anning Wei & Raymond M. Leuthold, 1998. "Long Agricultural Futures Prices: ARCH, Long Memory, or Chaos Processes?," Finance 9805001, University Library of Munich, Germany.
    8. Chatrath, Arjun & Adrangi, Bahram & Dhanda, Kanwalroop Kathy, 2002. "Are commodity prices chaotic?," Agricultural Economics, Blackwell, vol. 27(2), pages 123-137, August.
    9. Ignacio Olmeda & Joaquin Pérez, 1995. "Non-linear dynamics and chaos in the Spanish stock market," Investigaciones Economicas, Fundación SEPI, vol. 19(2), pages 217-248, May.
    10. Ioannis Andreadis & Athanasios D. Fragkou & Theodoros E. Karakasidis & Apostolos Serletis, 2023. "Nonlinear dynamics in Divisia monetary aggregates: an application of recurrence quantification analysis," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-17, December.
    11. Orlando Gomes, 2007. "Routes to chaos in macroeconomic theory," Journal of Economic Studies, Emerald Group Publishing, vol. 33(6), pages 437-468, January.
    12. Orlando Gomes, 2006. "Routes to chaos in macroeconomic theory," Journal of Economic Studies, Emerald Group Publishing, vol. 33(6), pages 437-468, November.
    13. 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.
    14. Matilla-García, Mariano & Marín, Manuel Ruiz, 2010. "A new test for chaos and determinism based on symbolic dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 76(3), pages 600-614, December.
    15. Kyrtsou, Catherine & Serletis, Apostolos, 2006. "Univariate tests for nonlinear structure," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 154-168, March.
    16. Ritesh Kumar Mishra & Sanjay Sehgal & N.R. Bhanumurthy, 2011. "A search for long‐range dependence and chaotic structure in Indian stock market," Review of Financial Economics, John Wiley & Sons, vol. 20(2), pages 96-104, May.
    17. 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.
    18. Steven R. Cunningham, 1993. "Unit Root Testing: A Critique From Chaos Theory," Review of Financial Economics, John Wiley & Sons, vol. 3(1), pages 1-18, September.
    19. Serletis, Apostolos & Uritskaya, Olga Y., 2007. "Detecting signatures of stochastic self-organization in US money and velocity measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(1), pages 281-291.
    20. Madhavan, Vinodh, 2013. "Nonlinearity in investment grade Credit Default Swap (CDS) Indices of US and Europe: Evidence from BDS and close-returns tests," Global Finance Journal, Elsevier, vol. 24(3), pages 266-279.

    More about this item

    Keywords

    Economic dynamics; nonlinearity; tests for chaos; chaos;
    All these keywords.

    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:tur:wpaper:25. 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: Daniele Pennesi (email available below). General contact details of provider: https://edirc.repec.org/data/dstorit.html .

    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.