  We consider the estimation of parametric fractional time series models in
which not only is the memory parameter unknown, but one may not know whether it
lies in the stationary/invertible region or the nonstationary or noninvertible
regions. In these circumstances, a proof of consistency (which is a
prerequisite for proving asymptotic normality) can be difficult owing to
nonuniform convergence of the objective function over a large admissible
parameter space. In particular, this is the case for the conditional sum of
squares estimate, which can be expected to be asymptotically efficient under
Gaussianity. Without the latter assumption, we establish consistency and
asymptotic normality for this estimate in case of a quite general univariate
model. For a multivariate model, we establish asymptotic normality of a
one-step estimate based on an initial $\sqrt{n}$-consistent estimate.
