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UNIT ROOT TESTING: A CRITIQUE FROM CHAOS THEORY
Author(s) -
Cunningham Steven R.
Publication year - 1993
Publication title -
review of financial economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 41
eISSN - 1873-5924
pISSN - 1058-3300
DOI - 10.1002/j.1873-5924.1993.tb00569.x
Subject(s) - unit root , spurious relationship , correlation dimension , mathematics , lyapunov exponent , nonlinear system , series (stratigraphy) , econometrics , chaotic , unit root test , white noise , autocorrelation , null hypothesis , chaos (operating system) , statistics , cointegration , computer science , mathematical analysis , artificial intelligence , physics , computer security , paleontology , fractal dimension , quantum mechanics , fractal , biology
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.