Quantile Periodograms (Complete Version)

Two periodogram-like functions, called quantile periodograms, are introduced for spectral analysis of time series. The quantile periodograms are constructed from trigonometric quantile regression and motivated by different interpretations of the ordinary periodogram. Analytical and numerical results demonstrate the capability of the quantile periodograms for providing an alternative and richer view of time-series data, enabling the detection of quantile-dependent spectral properties. A connection between the quantile periodograms and the level-crossing spectrum is established through an asymptotic analysis.