Am 01.02.2019 um 22:58 schrieb Allin Cottrell:
One way of interpreting urca is that it simply treats the
constant and unrestricted trend cases as personae non gratae. After all,
the options to the function allow only 3 of Johansen's 5 cases.
Yes, but the underlying fact that tended to be forgotten is that using
the unrestricted constant case only works conditional on a drift term in
the data that is actually there.
The attached example simulates the case of a trivial non-cointegrated
(but integrated) system without any drift (== no linear trend in the
data). The resulting 95% quantile matches urca's critical value (N-r_0 =
2 at 5%).
Using R's tsDyn, or gretl, or Stata with the unrestricted constant
choice on this example would yield biased tests (reject too often,
because there the critical value is around 15 instead of 18). This is
not the fault of these programs, because the user test spec is "wrong",
but in that sense R's urca is on the safe side.
But don't get me wrong: I think urca's communication is confusing and
the fact that you don't get the standard 5 cases there is not good.