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.