重尾下的幂律互相关估计
Power-law cross-correlations estimation under heavy tails
摘要：
在重尾分布下，研究了去趋势互相关分析、去趋势滑动平均互相关分析、高度互相关分析、平均周期图估计、互周期图估计和局部互Whittle估计等六种幂律互相关估计的性能.估计器的选择允许将这些估计器分成时域估计器和频域估计器。通过改变控制尾部行为的$α$稳定分布的特征指数，我们报告了几个有趣的发现。首先，频域估计实际上不受重尾偏置的影响。第二，时域估计器对于厚尾是向上偏置的，但是对于短序列，它们具有比另一组更低的估计方差。第三，具体的估计是更合适的分布特性和长度的分析系列。此外，我们提供了一个讨论的影响，这些结果的实证应用以及理论解释。
英文摘要：
We examine the performance of six estimators of the power-law cross-correlations -- the detrended cross-correlation analysis, the detrending moving-average cross-correlation analysis, the height cross-correlation analysis, the averaged periodogram estimator, the cross-periodogram estimator and the local cross-Whittle estimator -- under heavy-tailed distributions. The selection of estimators allows to separate these into the time and frequency domain estimators. By varying the characteristic exponent of the $α$-stable distributions which controls the tails behavior, we report several interesting findings. First, the frequency domain estimators are practically unaffected by heavy tails bias-wise. Second, the time domain estimators are upward biased for heavy tails but they have lower estimator variance than the other group for short series. Third, specific estimators are more appropriate depending on distributional properties and length of the analyzed series. In addition, we provide a discussion of implications of these results for empirical applications as well as theoretical explanations.
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