In this paper, we introduce a novel periodogram-like function called expectile periodograms, for detecting and estimating hidden periodicities in time series. The expectile periodograms are constructed from trigonometric expectile regression, in which a specially designed objective function is used to substitute the squared $l_2$ norm that leads to the ordinary periodograms. Analogous to quantile periodograms, the expectile periodograms provide a broader view of the time series than the ordinary periodograms by examining different expectile levels, while achieving higher computational efficiency. Simulations demonstrate the efficiency and robustness of the expectile periodograms in the presence of hidden periodicities. Finally, we leverage the inherent two-dimensional characteristics of the expectile periodograms and train a deep-learning (DL) model to classify the earthquake waveform data. Remarkably, our approach achieves higher classification testing accuracy when juxtaposed with alternative periodogram-based methodologies.

翻译：本文提出了一种新颖的类周期图函数，称为期望分位数周期图，用于检测和估计时间序列中的隐藏周期性。期望分位数周期图基于三角期望分位数回归构建，其中使用专门设计的损失函数替代了导致普通周期图的平方$l_2$范数。与分位数周期图类似，期望分位数周期图通过考察不同的期望分位数水平，提供了比普通周期图更全面的时间序列视角，同时实现了更高的计算效率。仿真实验验证了期望分位数周期图在存在隐藏周期性情况下的效率与鲁棒性。最后，我们利用期望分位数周期图固有的二维特性，训练了一个深度学习（DL）模型对地震波形数据进行分类。值得注意的是，与基于其他周期图的方法相比，我们的方法获得了更高的分类测试准确率。