A robust periodogram for high-resolution spectral analysis

Periodogram is an important tool for analyzing time series of mixed spectra that can be decomposed as sinusoids plus noise. While effective in many situations, the ordinary periodogram has two major shortcomings: it cannot resolve sinusoids whose frequencies are separated by less than 1 cycle per unit time; it does not possess sufficient robustness against heavy-tailed noise such as outliers. An alternative periodogram is introduced in this article with the aim of improving the frequency resolution as well as the robustness of the ordinary periodogram. The new periodogram, called bivariate ℓ1-periodogramℓ1-periodogram, is derived from the maximum likelihood method of multiple frequency estimation under the assumption of Laplace white noise. The desired high-resolution and robustness property of the bivariate ℓ1-periodogramℓ1-periodogram is confirmed by simulation studies. Superior statistical efficiency over alternative methods is also demonstrated.