  In this paper, we analyse the influence of estimating a constant term on the
bias of the conditional sum-of-squares (CSS) estimator in a stationary or
non-stationary type-II ARFIMA ($p_1$,$d$,$p_2$) model. We derive expressions
for the estimator's bias and show that the leading term can be easily removed
by a simple modification of the CSS objective function. We call this new
estimator the modified conditional sum-of-squares (MCSS) estimator. We show
theoretically and by means of Monte Carlo simulations that its performance
relative to that of the CSS estimator is markedly improved even for small
sample sizes. Finally, we revisit three classical short datasets that have in
the past been described by ARFIMA($p_1$,$d$,$p_2$) models with constant term,
namely the post-second World War real GNP data, the extended Nelson-Plosser
data, and the Nile data.
