Autori
Cavaliere, Giuseppe
Paruolo, Paolo
Fanelli, Luca

Titolo
Determining the number of cointegrating relations under rank constraints
Periodico
Università degli Studi dell'Insubria. Dipartimento di Economia. Quaderni di ricerca
Anno: 2001 - Fascicolo: 17 - Pagina iniziale: 1 - Pagina finale: 29

This paper discusses likelihood-ratio (LR) tests on the cointegrating (CI) rank which consider any possible dimension of the CI rank under the alternative. The trace test and lambda-max test are obtained as special cases. Limit quantiles for all the tests in the class are derived. It is found that any of these tests can be used to construct an estimator of the CI rank, with no differences in asymptotic properties when the alternative is fixed. The properties of the class of tests are investigated by local asymptotic analysis, a simulation study and two empirical illustrations. It is found that all the tests in the class have comparable power, which deteriorates substantially as the number of random walks increases. For one dimensional alternatives sufficiently far from the null, the trace tests is dominated by other tests in the class; this is in line with expectations based on the results of Andrews (1996, Econometrica) for LR tests in a stationary regression setup, when alternatives are one-sided. The tests in the class can also be arranged to give a constrained estimator of the CI rank, that restricts the minimum number of common trends. We find that mis-specification of the minimum number of common trends implies that the correct CI rank is selected with 0 limit probability. As a consequence, no value of the CI rank should be left untested, unless it can be excluded beyond any reasonable doubt.



Testo completo: http://eco.uninsubria.it/dipeco/quaderni/files/QF2001_17.pdf

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