Small Sample Properties of Certain Cointegration Test Statistics: A Monte Carlo Study
This paper reports on the result of a Monte Carlo study. The latter investigates the performance of various versions of the Conformity test (CCT) for the existence and rank of cointegration, as given in Johansen (J) (1988), (1991), and the stochastic trends qf(k,m) test (SW), as given in Stock and Watson (1988). The design of the experiments allows for small, medium, and large stationary roots, and one, two, and three unit roots. The largest system investigated is a quadrivariate VAR(4). Results based on the underlying normal theory indicate that the performance of the CCT is extremely good when the null hypothesis involves the sum of, or individual, (characteristic) roots, some of which are not zero; it does not perform reliably when the sum of the roots under the null involves, in truth, all zero roots, i.e. if we are testing a null that a root, say λ obeys λ > 0 and the null is in fact true, the test performs exceedingly well. If the null, however, is in fact false it has very little power. Results based on non-standard a symptotic theory for estimators of zero roots indicate that the CCT has very good power characteristics in detecting the rank of cointegration, but it exhibits some size distortions that can potentially lead to overestimation of the true cointegrating rank. On the other hand, both versions are robust to non-normal and dependent error structure. Such results generally hold for sample sizes 100 and 500. For sample of size 100, the LR test performs quite well, in terms of size, when the error process is Gaussian and when small and medium stationary roots are employed in the experimental design, but does rather poorly in terms of power. The problem is magnified with large stationary roots, and/or non-normal errors. The results improve, as expected, for sample size 500. The SW qf(k,m) test performs rather poorly overall, and cannot be recommended for use in empirical applications.
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