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Most of the long memory estimators for stationary fractionally integrated time series models are known to experience non-negligible bias in small and finite samples. Simple moment estimators are also vulnerable to such bias, but can easily be corrected. In this paper, we propose bias reduction methods for a lag-one sample autocorrelation-based moment estimator. In order to reduce the bias of the moment estimator, we explicitly obtain the exact bias of lag-one sample autocorrelation up to the order n−1. An example where the exact first-order bias can be noticeably more accurate than its asymptotic counterpart, even for large samples, is presented. We show via a simulation study that the proposed methods are promising and effective in reducing the bias of the moment estimator with minimal variance inflation.

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This is an author-produced, peer-reviewed version of this article. The final, definitive version of this document can be found online at Canadian Journal of Statistics, published by Wiley-Blackwell. Copyright restrictions may apply. DOI: 10.1002/cjs.10022

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