  This paper investigates the accuracy of bootstrap-based bias correction of
persistence measures for long memory fractionally integrated processes. The
bootstrap method is based on the semi-parametric sieve approach, with the
dynamics in the long memory process captured by an autoregressive
approximation. With a view to improving accuracy, the sieve method is also
applied to data pre-filtered by a semi-parametric estimate of the long memory
parameter. Both versions of the bootstrap technique are used to estimate the
finite sample distributions of the sample autocorrelation coefficients and the
impulse response coefficients and, in turn, to bias-adjust these statistics.
The accuracy of the resultant estimators in the case of the autocorrelation
coefficients is also compared with that yielded by analytical bias adjustment
methods when available. The basic sieve technique is seen to yield a reduction
in the bias of both persistence measures. The pre-filtered sieve produces a
substantial further reduction in the bias of the estimated impulse response
function, whilst the extra improvement yielded by pre-filtering in the case of
the sample autocorrelation function is shown to depend heavily on the accuracy
of the pre-filter.
