BENT NIELSEN
(2000)

'The asymptotic distribution of likelihood ratio test statistics for
cointegration in unstable vector autoregressive processes'

ABSTRACT:
When analysing cointegration in vector autoregressive models it is
usually assumed that (i) the number of cointegrating relations is not
smaller than what is tested for, (ii) the number of unit roots equals
the number of common stochastic trends, and (iii) the remaining
characteristic roots of the time series are stationary roots.
Condition (iii) could be violated in data from hyper-inflationary
economies and in connection with seasonally integrated data while
condition (ii) is not satisfied by processes which are integrated of
order two. Here it is proved that condition (iii) is redundant when
determining the cointegration rank whereas both condition (ii) and
(iii) are redundant when testing linear restrictions on the
cointegrating vector.