A New Spectral Analysis Procedure for the Identification of ULF Waves.

In the analysis of time series, one of the major diagnostic tools for the identification of periodic fluctuations is the frequency domain characterization via the power spectral density (PSD). Periodic signals manifest as enhancements relative to the continuous PSD. While harmonic analysis to identify the occurrence of periodic variations compared to a flat PSD are well established, there is a lack of standard techniques to assess the significance of a periodicity against colored noise, such as in the identification of ULF waves with respect to the colored PSD typically found in geophysical time series. Here, we present a new procedure based on the adaptive multitaper method (an open source IDL version is available at https://zenodo.org/record/3703168). This sophisticated non-parametric spectral analysis approach, suitable for colored PSD, provide an additional complex-valued regression model from which it is possible to estimate the amplitude and phase of the signals: the harmonic F test. A priori knowledge of the statistical properties of the multitaper PSD estimates allows a robust maximum likelihood fitting of different continuous PSD background models. Then, the best representation is selected via objective statistical criteria. Confidence thresholds are used to determine statistically significant PSD enhancements, that, when combined with the harmonic F test, provide robust estimates of the frequency of periodic oscillations occurring in the time series. After testing the performance of this method on Monte Carlo simulation of synthetic time series, we identify ULF fluctuations in magnetospheric field observations at geostationary orbit and in ground observatories. We present a brief tutorial of our procedure, and we discuss our analysis of the ULF fluctuations identified with our method.