Periodogram-based-40 estimators of the spectral density are known to exhibit distorted behavior in neighborhoods of the origin in case of so-called low frequency contamination, mimicking long-range dependence. This note quantifies the behavior of the estimator based on autoregressive approximations of order increasing with the sample size. Not surprisingly, the autoregressive spectral estimator is not consistent at the origin under ignored changes in the mean, but turns out to be consistent at non-zero frequencies. We furthermore show how a specific trimming of the fitted long autoregression can be used to restore consistency in the vicinity of the origin.

中文翻译：

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忽略均值变化下的自回归谱估计

已知基于周期图的 40 谱密度估计器在所谓的低频污染的情况下会在原点附近表现出扭曲的行为，模仿长程依赖性。本说明基于随样本大小增加的阶数的自回归近似来量化估计器的行为。毫不奇怪，自回归谱估计量在忽略均值变化的情况下在原点不一致，但在非零频率处结果是一致的。我们进一步展示了如何使用拟合长自回归的特定修剪来恢复原点附近的一致性。