Abstract In this paper, jackknife empirical likelihood is proposed to be applied in stationary time series models. By applying the jackknife method to Whittle estimator, we obtain new asymptotically independent pseudo samples which will be used to construct linear constraints for empirical likelihood. The jackknife empirical log-likelihood ratio is shown to follow a chi-square limiting distribution, which validates the corresponding confidence regions asymptotically. However, similar to the drawbacks of empirical likelihood, this method suffers from the non-definition problem and the inaccurate coverage probability in constructing confidence regions. So we further develop the adjusted jackknife empirical likelihood borrowing the idea of Chen et al. (2008) to improve the performance of the jackknife empirical likelihood. With a specific adjustment level, the adjusted jackknife empirical likelihood achieves a more high-order coverage precision than the classical jackknife empirical likelihood does and our simulations corroborate this point.

中文翻译：

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固定 ARMA 和 ARFIMA 模型的调整折刀经验似然

摘要 本文提出将折刀经验似然应用于平稳时间序列模型。通过将 jackknife 方法应用于 Whittle 估计器，我们获得了新的渐近独立的伪样本，这些伪样本将用于构建经验似然的线性约束。jackknife 经验对数似然比遵循卡方极限分布，渐近验证相应的置信区域。然而，类似于经验似然的缺点，该方法在构建置信区域时存在非定义问题和不准确的覆盖概率。因此，我们借用 Chen 等人的想法进一步开发了调整后的 jackknife 经验似然。(2008) 提高折刀经验似然的性能。