Detection and estimation of hidden periodicity in asymmetric noise by using quantile periodogram

This paper addresses the problem of detecting and estimating hidden periodicity from noisy observations when the noise distribution is asymmetric with heavy tail on one side. The ordinary periodogram is less effective in handling such noise. In this paper, we introduce an alternative periodogram-like function, called the quantile periodogram. The quantile periodogram is constructed from trigonometric regression where a specially designed objective function is used to substitute the squared ℓ₂ norm that leads to the ordinary periodogram. Simulation results are provided to demonstrate the superior performance of the quantile periodogram in comparison with the ordinary periodogram when the noise is asymmetrically distributed with a heavy tail. The asymptotic distribution of the quantile periodogram is derived under the white noise assumption. Extensions to the multivariate case and the complex case are also discussed.