This paper introduces a novel periodogram-like function, called the expectile periodogram, for modeling spectral features of time series and detecting hidden periodicities. The expectile periodogram is constructed from trigonometric expectile regression, in which a specially designed check function is used to substitute the squared $l_2$ norm that leads to the ordinary periodogram. The expectile periodogram retains the key properties of the ordinary periodogram as a frequency-domain representation of serial dependence in time series, while offering a more comprehensive understanding by examining the data across the entire range of expectile levels. We establish the asymptotic theory and investigate the relationship between the expectile periodogram and the so called expectile spectrum. Simulations demonstrate the efficiency of the expectile periodogram in the presence of hidden periodicities. Finally, by leveraging the inherent two-dimensional nature of the expectile periodogram, we train a deep learning (DL) model to classify earthquake waveform data. Remarkably, our approach outperforms alternative periodogram-based methods in terms of classification accuracy.

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，用于建模时间序列的谱特征并检测隐藏周期性。期望分位数周期图基于三角期望分位数回归构建，其中使用一个特殊设计的检验函数来替代导致普通周期图的平方 $l_2$ 范数。期望分位数周期图保留了普通周期图作为时间序列中序列依赖性的频域表示的关键特性，同时通过检查数据在整个期望分位数水平范围内的表现，提供了更全面的理解。我们建立了渐近理论，并研究了期望分位数周期图与所谓的期望分位数谱之间的关系。仿真实验证明了期望分位数周期图在存在隐藏周期性时的有效性。最后，利用期望分位数周期图固有的二维特性，我们训练了一个深度学习（DL）模型来分类地震波形数据。值得注意的是，我们的方法在分类准确率方面优于其他基于周期图的方法。