the nonparametric approach always works better than Johansen’s approach. Some preliminary
Monte Carlo simulations by Van Giersbergen (1994) and the author for a class of bivariate
cointegrated systems indicate that the small sample power of the nonparametric lambda-min
test may be quite poor compared with Johansen’s lambda-max test if the fit of the
cointegrating regression is low. In that case a full parametric approach may do a better job
than the nonparametric approach.
8.5. Concluding remarks
The above comparison of our nonparametric cointegration analysis with Johansen’s
approach shows that our nonparametric approach may be a useful addition to the menu of
cointegration tests. However, it should be stressed that our approach cannot completely
replace Johansen’s approach, because the latter provides additional information, in particular
regarding possible cointegration restrictions on the drift parameters, and the presence of linear
trends in the cointegration relations. Moreover, if one wishes to forecast a cointegrated
process or wants to do policy analysis (cf. Lutkepohl and Saikkonen, 1995), then Johansen’s
approach seems the only way to go. Thus, rather than being substitutes, the two approaches
are complements.
References
Anderson,S.A., H.K.Brons and S.T.Jensen, 1983, Distribution of eigenvalues in
multivariate statistical analysis, Annals of Statistics 11, 392-415.
Bierens,H.J., 1993, Higher-order sample autocorrelations and the unit root hypothesis,
Journal of Econometrics 57, 137-160.
Bierens,H.J., 1994, Topics in advanced econometrics: estimation, testing, and specification
of cross-section and time series models (Cambridge, U.K.: Cambridge University
Press).
Bierens,H.J. and S.Guo, 1993, Testing stationarity and trend stationarity against the unit
root hypothesis, Econometric Reviews 12, 1-32.
Billingsley, P., 1968, Convergence of probability measures (New York: John Wiley).
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