Corrigendum to: A Generalised Fractional Differencing Bootstrap for Long Memory Processes (Journal of Time Series Analysis, (2019), 40, 4, (467-492), 10.1111/jtsa.12460)

On page 475, Assumption 2 and the immediately subsequent Remark 13 should be replaced by the alternative versions of these given below. We are grateful to Morten Nielsen for pointing this out to us. Assumption 2. Suppose that Yt is generated by (1), and let Assumption 1 hold. Then, we assume that there exists an estimator, (Formula presented.), of the true fractional integration parameter, d, which satisfies the condition that (Formula presented.). Remark 13. Assumption 2 does not specify any particular method for estimating d. Obvious candidate estimators to consider are the LW and ELW estimators discussed in Section 2. For consistency, the bandwidth, m, used for the LW estimator must satisfy the condition that (Formula presented.), while for ELW the required rate on m is that (Formula presented.), for any 0. For ELW the range of permissible values in the optimisation in (3) is such that (Formula presented.), although note that this does not restrict the value of d itself. The full set of required conditions for consistency are given in Assumptions A1 to A4 of Robinson (1995) for the LW estimator and in Assumptions 1 to 5 of Phillips and Shimotsu (2005) for the ELW estimator. Assumption 2, however, requires the stronger concept of convergence in mean square. This would need to be verified for any given estimator. Given convergence in distribution, a sufficient condition for Assumption 2 to hold is that (Formula presented.) is uniformly integrable.