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Unit Root Testing: A Critique From Chaos Theory

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  • 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
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    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.
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    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.

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