  We use the jackknife to bias correct the log-periodogram regression(LPR)
estimator of the fractional parameter in a stationary fractionally integrated
model. The weights for the jackknife estimator are chosen in such a way that
bias reduction is achieved without the usual increase in asymptotic variance,
with the estimator viewed as `optimal' in this sense. The theoretical results
are valid under both the non-overlapping and moving-block sub-sampling schemes
that can be used in the jackknife technique, and do not require the assumption
of Gaussianity for the data generating process. A Monte Carlo study explores
the finite sample performance of different versions of the jackknife estimator,
under a variety of scenarios. The simulation experiments reveal that when the
weights are constructed using the parameter values of the true data generating
process, a version of the optimal jackknife estimator almost always
out-performs alternative semi-parametric bias-corrected estimators. A feasible
version of the jackknife estimator, in which the weights are constructed using
estimates of the unknown parameters, whilst not dominant overall, is still the
least biased estimator in some cases. Even when misspecified short run dynamics
are assumed in the construction of the weights, the feasible jackknife still
shows significant reduction in bias under certain designs. As is not
surprising, parametric maximum likelihood estimation out-performs all
semi-parametric methods when the true values of the short memory parameters are
known, but is dominated by the semi-parametric methods (in terms of bias) when
the short memory parameters need to be estimated, and in particular when the
model is misspecified.

Methodology