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Expansions for approximate maximum likelihood estimators of the fractional difference parameter

机译:分数差分参数的近似最大似然估计的展开

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This paper derives second-order expansions for the distributions of the Whittle and profile plug-in maximum likelihood estimators of the fractional difference parameter in the 'Autoregressive Fractionally Integrated Moving Average of order (0, d, 0)' with unknown mean and variance. Both estimators are shown to be second-order pivotal. This extends earlier findings of Lieberman and Phillips (2004a, Econometric Theory, 20, 464-84), who derived expansions for the Gaussian maximum likelihood estimator under the assumption that the mean and variance are known. One implication of the results is that the parametric bootstrap upper one-sided confidence interval provides an o(n~(-1) ln n) improvement over the delta method. For statistics that are not second-order pivotal, the improvement is generally only of the order o(n~(-1/2) ln n).
机译:本文推导了在具有均值和方差未知的“阶(0,d,0)的自回归分数积分移动平均值”中分数差参数的Whittle和轮廓插件最大似然估计的分布的二阶展开。这两个估计量均显示为二阶枢轴。这扩展了Lieberman和Phillips(2004a,Econometric Theory,20,464-84)的早期发现,他们在均值和方差已知的假设下得出了高斯最大似然估计的展开式。结果的一个暗示是,参数自举的上部单侧置信区间提供了相对于增量法的o(n〜(-1)ln n)改进。对于不是二阶关键点的统计量,通常只将改进程度提高到o(n〜(-1/2)ln n)。

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