非对称胡贝尔周期图 (Asymmetric Huber Periodogram)

This paper introduces a novel spectral M-estimator, called the asymmetric Huber periodogram (AHP), for periodicity detection in time series. The AHP is constructed from trigonometric asymmetric Huber regression, where a specially designed check function is used to substitute the squared L2 norm that defines the ordinary periodogram (PG). The AHP is statistically more efficient than the quantile periodogram (QP), while offering a more comprehensive picture than the Huber periodogram (HP) by examining the data across the entire range of the asymmetric parameter. We prove the theoretical properties of the AHP and investigate the relationship between the AHP and the so-called asymmetric Huber spectrum (AHS). Finally, simulations and three real-world data examples demonstrate that the AHP's capability in detecting periodicity and its robustness against outliers.

翻译：本文提出了一种新颖的谱M估计量，称为非对称胡贝尔周期图（AHP），用于时间序列中的周期性检测。AHP基于三角非对称胡贝尔回归构建，其中采用专门设计的检验函数替代了定义普通周期图（PG）的平方L2范数。在统计效率上，AHP优于分位数周期图（QP），同时通过考察不对称参数在整个取值范围内的数据，提供了比胡贝尔周期图（HP）更全面的分析视角。我们证明了AHP的理论性质，并探讨了AHP与所谓非对称胡贝尔谱（AHS）之间的关系。最后，通过仿真实验和三个真实世界数据案例，验证了AHP在周期性检测方面的能力及其对异常值的鲁棒性。