论文标题
（在）有限变化时间序列的时间域中的远程依赖性检测
Detection of Long Range Dependence in the Time Domain for (In)Finite-Variance Time Series
论文作者
论文摘要
时间序列的远程依赖性（LRD）的经验检测通常包括确定内存参数$ d $的估计是否对应于LRD。令人惊讶的是，文献为$ d $提供了众多的光谱域估计器，但是时域中只有少数估计器。此外，后一个估计器因依靠视觉检查来确定观察窗口$ [n_1，n_2] $而受到批评，以进行线性回归。许多时间序列模型通常会缺少$ n_1 $和$ n_2 $的理论动机选择。 在本文中，我们采用了众所周知的差异图估计器，并在$ [n_1，n_2] $上提供严格的渐近条件，以确保根据LRD的估计器的一致性。我们为大型平方综合时间序列模型建立了这些条件。这个大型类使人们能够使用方差图估计量来检测无限差异时间序列的LRD（在适当的转换之后）。因此，对于无限变化时间序列的LRD检测是我们论文的另一个新颖性。一项仿真研究表明，方差图估计器可以比流行的光谱域GPH估计器更好地检测LRD。
Empirical detection of long range dependence (LRD) of a time series often consists of deciding whether an estimate of the memory parameter $d$ corresponds to LRD. Surprisingly, the literature offers numerous spectral domain estimators for $d$ but there are only a few estimators in the time domain. Moreover, the latter estimators are criticized for relying on visual inspection to determine an observation window $[n_1, n_2]$ for a linear regression to run on. Theoretically motivated choices of $n_1$ and $n_2$ are often missing for many time series models. In this paper, we take the well-known variance plot estimator and provide rigorous asymptotic conditions on $[n_1, n_2]$ to ensure the estimator's consistency under LRD. We establish these conditions for a large class of square-integrable time series models. This large class enables one to use the variance plot estimator to detect LRD for infinite-variance time series (after suitable transformation). Thus, detection of LRD for infinite-variance time series is another novelty of our paper. A simulation study indicates that the variance plot estimator can detect LRD better than the popular spectral domain GPH estimator.
