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Abstract:
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Many 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. To reduce the bias of the moment estimator, we explicitly obtain the exact bias of lag-one sample autocorrelation up to the order 1/n. 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. The proposed methods are applied to the northern hemisphere data.
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