A bootstrap methodology, first proposed in a restricted form by Kapetanios and Papailias (2011), suitable for use with stationary and nonstationary fractionally integrated time series is further developed in this paper. The resampling algorithm involves estimating the degree of fractional integration, applying the fractional differencing operator, resampling the resulting approximation to the underlying short memory series and, finally, cumulating to obtain a resample of the original fractionally integrated process. While a similar approach based on differencing has been independently proposed in the literature for stationary fractionally integrated processes using the sieve bootstrap by Poskitt, Grose and Martin (2015), we extend it to allow for general bootstrap schemes including blockwise bootstraps. Further, we show that it can also be validly used for nonstationary fractionally integrated processes. We establish asymptotic validity results for the general method and provide simulation evidence which highlights a number of favourable aspects of its finite sample performance, relative to other commonly used bootstrap methods.

中文翻译：

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长记忆过程的广义分数差分引导

本文进一步开发了一种自举方法，该方法首先由 Kapetanios 和 Papailias (2011) 以受限形式提出，适用于平稳和非平稳部分积分时间序列。重采样算法包括估计分数积分的程度、应用分数差分算子、对所得到的近似值重新采样到底层的短记忆序列，最后累积以获得原始分数积分过程的重采样。虽然 Poskitt、Grose 和 Martin（2015 年）在文献中独立提出了一种基于差分的类似方法，用于使用筛子引导的静止分数集成过程，但我们将其扩展为允许包括块状引导在内的一般引导方案。更多，我们表明它也可以有效地用于非平稳部分积分过程。我们为一般方法建立渐近有效性结果，并提供模拟证据，突出其有限样本性能的许多有利方面，相对于其他常用的自举方法。