Expectile Periodograms

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.