IDEAS home Printed from https://ideas.repec.org/a/wly/revfec/v3y1993i1p1-18.html
   My bibliography  Save this article

Unit Root Testing: A Critique From Chaos Theory

Author

Listed:
  • Steven R. Cunningham

Abstract

A counter‐example from chaos theory is used to challenge the augmented Dickey‐Fuller (ADF) test and common prewhitening techniques. The ADF test is applied to data constructed from a fully deterministic nonlinear (chaotic) process. The null hypothesis, that a unit root is present, cannot be rejected; “stationarity” is achieved by prewhitening. The largest Lyapunov exponent and the correlation dimension are estimated for the original and conditioned series in efforts to detect the nonlinearity and ascertain information regarding its specification. This is repeated in the presence of additive white noise. In no case is the procedure successful, nor is misspecification avoided. Along the way, the tests for nonlinearity provide evidence in support of the results of Nelson and Plosser (1982), that the removal of deterministic trends from time series that appear to be unit root processes can lead to spurious results.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:revfec:v:3:y:1993:i:1:p:1-18
    DOI: 10.1002/j.1873-5924.1993.tb00569.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/j.1873-5924.1993.tb00569.x
    Download Restriction: no
    File URL: https://libkey.io/10.1002/j.1873-5924.1993.tb00569.x?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
    ---><---

    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. Hall, Robert E, 1978. "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 971-987, December.
    3. Brock, W. A., 1986. "Distinguishing random and deterministic systems: Abridged version," Journal of Economic Theory, Elsevier, vol. 40(1), pages 168-195, October.
    4. Godfrey, Leslie G, 1978. "Testing for Higher Order Serial Correlation in Regression Equations When the Regressors Include Lagged Dependent Variables," Econometrica, Econometric Society, vol. 46(6), pages 1303-1310, November.
    5. 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.
    6. Gregory Mankiw, N. & Shapiro, Matthew D., 1985. "Trends, random walks, and tests of the permanent income hypothesis," Journal of Monetary Economics, Elsevier, vol. 16(2), pages 165-174, September.
    7. West, Kenneth D., 1988. "The insensitivity of consumption to news about income," Journal of Monetary Economics, Elsevier, vol. 21(1), pages 17-33, January.
    8. Ramsey, James B. & Yuan, Hsiao-Jane, 1987. "The Statistical Properties of Dimension Calculations Using Small Data Sets," Working Papers 87-20, C.V. Starr Center for Applied Economics, New York University.
    9. William J. Baumol & Richard E. Quandt, 1985. "Chaos Models and Their Implications for Forecasting," Eastern Economic Journal, Eastern Economic Association, vol. 11(1), pages 3-15, Jan-Mar.
    10. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    11. Frank, Murray Z. & Stengos, Thanasis, 1988. "Some evidence concerning macroeconomic chaos," Journal of Monetary Economics, Elsevier, vol. 22(3), pages 423-438.
    12. Raj, Baldev & Siklos, Pierre L, 1988. "Some Qualms about the Test of the Institutional Hypothesis of the Long-run Behavior of Velocity," Economic Inquiry, Western Economic Association International, vol. 26(3), pages 537-545, July.
    13. Frank, Murray Z & Stengos, Thanasis, 1988. "Chaotic Dynamics in Economic Time-Series," Journal of Economic Surveys, Wiley Blackwell, vol. 2(2), pages 103-133.
    14. 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.
    15. Torre, V, 1977. "Existence of Limit Cycles and Control in Complete Keynesian System by Theory of Bifurcations," Econometrica, Econometric Society, vol. 45(6), pages 1457-1466, September.
    16. 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.
    17. Day, Richard H, 1982. "Irregular Growth Cycles," American Economic Review, American Economic Association, vol. 72(3), pages 406-414, June.
    18. 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.
    19. 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.
    20. 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. Anning Wei & Raymond M. Leuthold, 1998. "Long Agricultural Futures Prices: ARCH, Long Memory, or Chaos Processes?," Finance 9805001, University Library of Munich, Germany.

    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, 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.
    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. Nijkamp, Peter & Reggiani, Aura, 1995. "Non-linear evolution of dynamic spatial systems. The relevance of chaos and ecologically-based models," Regional Science and Urban Economics, Elsevier, vol. 25(2), pages 183-210, April.
    4. Chatrath, Arjun & Adrangi, Bahram & Dhanda, Kanwalroop Kathy, 2002. "Are commodity prices chaotic?," Agricultural Economics, Blackwell, vol. 27(2), pages 123-137, August.
    5. Luis A. Aguirre & Antonio Aguirre, 1997. "A tutorial introduction to nonlinear dynamics in economics," Nova Economia, Economics Department, Universidade Federal de Minas Gerais (Brazil), vol. 7(2), pages 9-47.
    6. Takala, Kari & Virén, Matti, 1995. "Testing nonlinear dynamics, long memory and chaotic behaviour with macroeconomic data," Bank of Finland Research Discussion Papers 9/1995, Bank of Finland.
    7. 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.
    8. Takala, Kari & Virén, Matti, 1995. "Testing nonlinear dynamics, long memory and chaotic behaviour with macroeconomic data," Research Discussion Papers 9/1995, Bank of Finland.
    9. repec:zbw:bofrdp:1995_009 is not listed on IDEAS
    10. 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.
    11. 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.
    12. A. Corcos & J-P Eckmann & A. Malaspinas & Y. Malevergne & D. Sornette, 2002. "Imitation and contrarian behaviour: hyperbolic bubbles, crashes and chaos," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 264-281.
    13. David F. Hendry, 2013. "Retrospective on ‘Econometric Modelling: The Consumption Function in Retrospect’, Scottish Journal of Political Economy, 30 (1983), 193–220'," Scottish Journal of Political Economy, Scottish Economic Society, vol. 60(5), pages 523-525, November.
    14. Nijkamp, P. & Poot, J., 1991. "Lessons from non-linear dynamic economics," Serie Research Memoranda 0105, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    15. Olmedo, Elena, 2011. "Is there chaos in the Spanish labour market?," Chaos, Solitons & Fractals, Elsevier, vol. 44(12), pages 1045-1053.
    16. Gregory, Allan W. & McCurdy, Thomas H., 1984. "Testing the unbiasedness hypothesis in the forward foreign exchange market: A specification analysis," Journal of International Money and Finance, Elsevier, vol. 3(3), pages 357-368, December.
    17. Christiano, Lawrence J. & Eichenbaum, Martin, 1990. "Unit roots in real GNP: Do we know, and do we care?," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 32(1), pages 7-61, January.
    18. Ahmad Yamin S & Paya Ivan, 2020. "Temporal aggregation of random walk processes and implications for economic analysis," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 24(2), pages 1-20, April.
    19. Peat, Maurice & Stevenson, Max, 1996. "Asymmetry in the business cycle: Evidence from the Australian labour market," Journal of Economic Behavior & Organization, Elsevier, vol. 30(3), pages 353-368, September.
    20. Gilbert Colletaz & Jean-Pierre Gourlaouen, 1990. "Coïntégration et structure par terme des taux d'intérêt," Revue Économique, Programme National Persée, vol. 41(4), pages 687-712.
    21. John Y. Campbell & Pierre Perron, 1991. "Pitfalls and Opportunities: What Macroeconomists Should Know about Unit Roots," NBER Chapters, in: NBER Macroeconomics Annual 1991, Volume 6, pages 141-220, National Bureau of Economic Research, Inc.

    More about this item

    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:wly:revfec:v:3:y:1993:i:1:p:1-18. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1873-5924 .

    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.