  Employing recent results of Robinson (2005) we consider the asymptotic
properties of conditional-sum-of-squares (CSS) estimates of parametric models
for stationary time series with long memory. CSS estimation has been considered
as a rival to Gaussian maximum likelihood and Whittle estimation of time series
models. The latter kinds of estimate have been rigorously shown to be
asymptotically normally distributed in case of long memory. However, CSS
estimates, which should have the same asymptotic distributional properties
under similar conditions, have not received comparable treatment: the
truncation of the infinite autoregressive representation inherent in CSS
estimation has been essentially ignored in proofs of asymptotic normality.
Unlike in short memory models it is not straightforward to show the truncation
has negligible effect.
