Bias Correction of Persistence Measures in Fractionally Integrated Models

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 (raw) 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.